pymatgen.analysis.graphs — pymatgen 2020.7.3 documentation

# Source code for pymatgen.analysis.graphs

    # coding: utf-8
    # Copyright (c) Pymatgen Development Team.
    # Distributed under the terms of the MIT License.

    """
    Module for graph representations of crystals.
    """

    import warnings
    import subprocess
    import numpy as np
    import os.path
    import copy
    from itertools import combinations

    from pymatgen.core import Structure, Lattice, PeriodicSite, Molecule
    from pymatgen.core.structure import FunctionalGroups
    from pymatgen.util.coord import lattice_points_in_supercell
    from pymatgen.vis.structure_vtk import EL_COLORS

    from monty.json import MSONable
    from monty.os.path import which
    from operator import itemgetter
    from collections import namedtuple, defaultdict
    from scipy.spatial import KDTree
    from scipy.stats import describe

    import networkx as nx
    import networkx.algorithms.isomorphism as iso
    from networkx.readwrite import json_graph
    from networkx.drawing.nx_agraph import write_dot

    try:
        import igraph
        IGRAPH_AVAILABLE = True
    except ImportError:
        IGRAPH_AVAILABLE = False

    import logging

    logger = logging.getLogger(__name__)
    logger.setLevel(logging.INFO)

    __author__ = "Matthew Horton, Evan Spotte-Smith, Samuel Blau"
    __version__ = "0.1"
    __maintainer__ = "Matthew Horton"
    __email__ = "mkhorton@lbl.gov"
    __status__ = "Production"
    __date__ = "August 2017"

    ConnectedSite = namedtuple('ConnectedSite', 'site, jimage, index, weight, dist')

    def _compare(g1, g2, i1, i2):
        """
        Helper function called by isomorphic to ensure comparison of node identities.
        """
        return g1.vs[i1]['species'] == g2.vs[i2]['species']

    def _igraph_from_nxgraph(graph):
        """
        Helper function that converts a networkx graph object into an igraph graph object.
        """
        nodes = graph.nodes(data=True)
        new_igraph = igraph.Graph()
        for node in nodes:
            new_igraph.add_vertex(name=str(node[0]), species=node[1]["specie"], coords=node[1]["coords"])
        new_igraph.add_edges([(str(edge[0]), str(edge[1])) for edge in graph.edges()])
        return new_igraph

    def _isomorphic(frag1, frag2):
        """
        Internal function to check if two graph objects are isomorphic, using igraph if
        if is available and networkx if it is not.
        """
        f1_nodes = frag1.nodes(data=True)
        f2_nodes = frag2.nodes(data=True)
        if len(f1_nodes) != len(f2_nodes):
            return False
        f2_edges = frag2.edges()
        if len(f2_edges) != len(f2_edges):
            return False
        f1_comp_dict = {}
        f2_comp_dict = {}
        for node in f1_nodes:
            if node[1]["specie"] not in f1_comp_dict:
                f1_comp_dict[node[1]["specie"]] = 1
            else:
                f1_comp_dict[node[1]["specie"]] += 1
        for node in f2_nodes:
            if node[1]["specie"] not in f2_comp_dict:
                f2_comp_dict[node[1]["specie"]] = 1
            else:
                f2_comp_dict[node[1]["specie"]] += 1
        if f1_comp_dict != f2_comp_dict:
            return False
        if IGRAPH_AVAILABLE:
            ifrag1 = _igraph_from_nxgraph(frag1)
            ifrag2 = _igraph_from_nxgraph(frag2)
            return ifrag1.isomorphic_vf2(ifrag2, node_compat_fn=_compare)
        else:
            nm = iso.categorical_node_match("specie", "ERROR")
            return nx.is_isomorphic(frag1.to_undirected(), frag2.to_undirected(), node_match=nm)

    class StructureGraph(MSONable):
        """
        This is a class for annotating a Structure with
        bond information, stored in the form of a graph. A "bond" does
        not necessarily have to be a chemical bond, but can store any
        kind of information that connects two Sites.
        """

        def __init__(self, structure, graph_data=None):
            """
            If constructing this class manually, use the `with_empty_graph`
            method or `with_local_env_strategy` method (using an algorithm
            provided by the `local_env` module, such as O'Keeffe).

            This class that contains connection information:
            relationships between sites represented by a Graph structure,
            and an associated structure object.

            This class uses the NetworkX package to store and operate
            on the graph itself, but contains a lot of helper methods
            to make associating a graph with a given crystallographic
            structure easier.

            Use cases for this include storing bonding information,
            NMR J-couplings, Heisenberg exchange parameters, etc.

            For periodic graphs, class stores information on the graph
            edges of what lattice image the edge belongs to.

            :param structure: a Structure object

            :param graph_data: dict containing graph information in
                dict format (not intended to be constructed manually,
            see as_dict method for format)
            """

            if isinstance(structure, StructureGraph):
                # just make a copy from input
                graph_data = structure.as_dict()['graphs']

            self.structure = structure
            self.graph = nx.readwrite.json_graph.adjacency_graph(graph_data)

            # tidy up edge attr dicts, reading to/from json duplicates
            # information
            for u, v, k, d in self.graph.edges(keys=True, data=True):
                if 'id' in d:
                    del d['id']
                if 'key' in d:
                    del d['key']
                # ensure images are tuples (conversion to lists happens
                # when serializing back from json), it's important images
                # are hashable/immutable
                if 'to_jimage' in d:
                    d['to_jimage'] = tuple(d['to_jimage'])
                if 'from_jimage' in d:
                    d['from_jimage'] = tuple(d['from_jimage'])

        @classmethod
        def with_empty_graph(cls, structure, name="bonds",
                             edge_weight_name=None,
                             edge_weight_units=None):
            """
            Constructor for StructureGraph, returns a StructureGraph
            object with an empty graph (no edges, only nodes defined
            that correspond to Sites in Structure).

            :param structure (Structure):
            :param name (str): name of graph, e.g. "bonds"
            :param edge_weight_name (str): name of edge weights,
                e.g. "bond_length" or "exchange_constant"
            :param edge_weight_units (str): name of edge weight units
                e.g. "Å" or "eV"
            :return (StructureGraph):
            """

            if edge_weight_name and (edge_weight_units is None):
                raise ValueError("Please specify units associated "
                                 "with your edge weights. Can be "
                                 "empty string if arbitrary or "
                                 "dimensionless.")

            # construct graph with one node per site
            # graph attributes don't change behavior of graph,
            # they're just for book-keeping
            graph = nx.MultiDiGraph(edge_weight_name=edge_weight_name,
                                    edge_weight_units=edge_weight_units,
                                    name=name)
            graph.add_nodes_from(range(len(structure)))

            graph_data = json_graph.adjacency_data(graph)

            return cls(structure, graph_data=graph_data)

        @staticmethod
        def with_edges(structure, edges):
            """
            Constructor for MoleculeGraph, using pre-existing or pre-defined edges
            with optional edge parameters.

            :param molecule: Molecule object
            :param edges: dict representing the bonds of the functional
                group (format: {(from_index, to_index, from_image, to_image): props},
                where props is a dictionary of properties, including weight.
                Props should be None if no additional properties are to be
                specified.
            :return: sg, a StructureGraph
            """

            sg = StructureGraph.with_empty_graph(structure, name="bonds",
                                                 edge_weight_name="weight",
                                                 edge_weight_units="")

            for edge, props in edges.items():

                try:
                    from_index = edge[0]
                    to_index = edge[1]
                    from_image = edge[2]
                    to_image = edge[3]
                except TypeError:
                    raise ValueError("Edges must be given as (from_index, to_index,"
                                     " from_image, to_image) tuples")

                if props is not None:
                    if "weight" in props.keys():
                        weight = props["weight"]
                        del props["weight"]
                    else:
                        weight = None

                    if len(props.items()) == 0:
                        props = None
                else:
                    weight = None

                nodes = sg.graph.nodes
                if not (from_index in nodes and to_index in nodes):
                    raise ValueError("Edges cannot be added if nodes are not"
                                     " present in the graph. Please check your"
                                     " indices.")

                sg.add_edge(from_index, to_index, from_jimage=from_image,
                            to_jimage=to_image, weight=weight,
                            edge_properties=props)

            sg.set_node_attributes()
            return sg

        @staticmethod
        def with_local_env_strategy(structure, strategy, weights=False):
            """
            Constructor for StructureGraph, using a strategy
            from :Class: `pymatgen.analysis.local_env`.

            :param structure: Structure object
            :param strategy: an instance of a
                :Class: `pymatgen.analysis.local_env.NearNeighbors` object
            :param weights: if True, use weights from local_env class
                (consult relevant class for their meaning)
            :return:
            """

            if not strategy.structures_allowed:
                raise ValueError("Chosen strategy is not designed for use with structures! "
                                 "Please choose another strategy.")

            sg = StructureGraph.with_empty_graph(structure, name="bonds")

            for n, neighbors in enumerate(strategy.get_all_nn_info(structure)):
                for neighbor in neighbors:
                    # local_env will always try to add two edges
                    # for any one bond, one from site u to site v
                    # and another form site v to site u: this is
                    # harmless, so warn_duplicates=False
                    sg.add_edge(from_index=n,
                                from_jimage=(0, 0, 0),
                                to_index=neighbor['site_index'],
                                to_jimage=neighbor['image'],
                                weight=neighbor['weight'] if weights else None,
                                warn_duplicates=False)

            return sg

        @property
        def name(self):
            """
            :return: Name of graph
            """
            return self.graph.graph['name']

        @property
        def edge_weight_name(self):
            """
            :return: Name of the edge weight property of graph
            """
            return self.graph.graph['edge_weight_name']

        @property
        def edge_weight_unit(self):
            """
            :return: Units of the edge weight property of graph
            """
            return self.graph.graph['edge_weight_units']

        def add_edge(self, from_index, to_index,
                     from_jimage=(0, 0, 0), to_jimage=None,
                     weight=None, warn_duplicates=True,
                     edge_properties=None):
            """
            Add edge to graph.

            Since physically a 'bond' (or other connection
            between sites) doesn't have a direction, from_index,
            from_jimage can be swapped with to_index, to_jimage.

            However, images will always always be shifted so that
            from_index < to_index and from_jimage becomes (0, 0, 0).

            :param from_index: index of site connecting from
            :param to_index: index of site connecting to
            :param from_jimage (tuple of ints): lattice vector of periodic
                image, e.g. (1, 0, 0) for periodic image in +x direction
            :param to_jimage (tuple of ints): lattice vector of image
            :param weight (float): e.g. bond length
            :param warn_duplicates (bool): if True, will warn if
                trying to add duplicate edges (duplicate edges will not
                be added in either case)
            :param edge_properties (dict): any other information to
                store on graph edges, similar to Structure's site_properties
            :return:
            """

            # this is not necessary for the class to work, but
            # just makes it neater
            if to_index < from_index:
                to_index, from_index = from_index, to_index
                to_jimage, from_jimage = from_jimage, to_jimage

            # constrain all from_jimages to be (0, 0, 0),
            # initial version of this class worked even if
            # from_jimage != (0, 0, 0), but making this
            # assumption simplifies logic later
            if not np.array_equal(from_jimage, (0, 0, 0)):
                shift = from_jimage
                from_jimage = np.subtract(from_jimage, shift)
                to_jimage = np.subtract(to_jimage, shift)

            # automatic detection of to_jimage if user doesn't specify
            # will try and detect all equivalent images and add multiple
            # edges if appropriate
            if to_jimage is None:
                # assume we want the closest site
                warnings.warn("Please specify to_jimage to be unambiguous, "
                              "trying to automatically detect.")
                dist, to_jimage = self.structure[from_index] \
                    .distance_and_image(self.structure[to_index])
                if dist == 0:
                    # this will happen when from_index == to_index,
                    # typically in primitive single-atom lattices
                    images = [1, 0, 0], [0, 1, 0], [0, 0, 1]
                    dists = []
                    for image in images:
                        dists.append(self.structure[from_index]
                                     .distance_and_image(self.structure[from_index],
                                                         jimage=image)[0])
                    dist = min(dists)
                equiv_sites = self.structure.get_neighbors_in_shell(self.structure[from_index].coords,
                                                                    dist,
                                                                    dist * 0.01,
                                                                    include_index=True)
                for site, dist, to_index in equiv_sites:
                    to_jimage = np.subtract(site.frac_coords, self.structure[from_index].frac_coords)
                    to_jimage = np.round(to_jimage).astype(int)
                    self.add_edge(from_index=from_index, from_jimage=(0, 0, 0),
                                  to_jimage=to_jimage, to_index=to_index)
                return

            # sanitize types
            from_jimage, to_jimage = tuple(map(int, from_jimage)), tuple(map(int, to_jimage))
            from_index, to_index = int(from_index), int(to_index)

            # check we're not trying to add a duplicate edge
            # there should only ever be at most one edge
            # between a given (site, jimage) pair and another
            # (site, jimage) pair
            existing_edge_data = self.graph.get_edge_data(from_index, to_index)
            if existing_edge_data:
                for key, d in existing_edge_data.items():
                    if d["to_jimage"] == to_jimage:
                        if warn_duplicates:
                            warnings.warn("Trying to add an edge that already exists from "
                                          "site {} to site {} in {}.".format(from_index,
                                                                             to_index,
                                                                             to_jimage))
                        return

            # generic container for additional edge properties,
            # similar to site properties
            edge_properties = edge_properties or {}

            if weight:
                self.graph.add_edge(from_index, to_index,
                                    to_jimage=to_jimage,
                                    weight=weight,
                                    **edge_properties)
            else:
                self.graph.add_edge(from_index, to_index,
                                    to_jimage=to_jimage,
                                    **edge_properties)

        def insert_node(self, i, species, coords, coords_are_cartesian=False,
                        validate_proximity=False, site_properties=None, edges=None):
            """
            A wrapper around Molecule.insert(), which also incorporates the new
            site into the MoleculeGraph.

            :param i: Index at which to insert the new site
            :param species: Species for the new site
            :param coords: 3x1 array representing coordinates of the new site
            :param coords_are_cartesian: Whether coordinates are cartesian.
                Defaults to False.
            :param validate_proximity: For Molecule.insert(); if True (default
                False), distance will be checked to ensure that site can be safely
                added.
            :param site_properties: Site properties for Molecule
            :param edges: List of dicts representing edges to be added to the
                MoleculeGraph. These edges must include the index of the new site i,
                and all indices used for these edges should reflect the
                MoleculeGraph AFTER the insertion, NOT before. Each dict should at
                least have a "to_index" and "from_index" key, and can also have a
                "weight" and a "properties" key.
            :return:
            """

            self.structure.insert(i, species, coords,
                                  coords_are_cartesian=coords_are_cartesian,
                                  validate_proximity=validate_proximity,
                                  properties=site_properties)

            mapping = {}
            for j in range(len(self.structure) - 1):
                if j < i:
                    mapping[j] = j
                else:
                    mapping[j] = j + 1
            nx.relabel_nodes(self.graph, mapping, copy=False)

            self.graph.add_node(i)
            self.set_node_attributes()

            if edges is not None:
                for edge in edges:
                    try:
                        self.add_edge(edge["from_index"], edge["to_index"],
                                      from_jimage=(0, 0, 0),
                                      to_jimage=edge["to_jimage"],
                                      weight=edge.get("weight", None),
                                      edge_properties=edge.get("properties", None))
                    except KeyError:
                        raise RuntimeError("Some edges are invalid.")

        def set_node_attributes(self):
            """
            Gives each node a "specie" and a "coords" attribute, updated with the
            current species and coordinates.

            :return:
            """

            species = {}
            coords = {}
            properties = {}
            for node in self.graph.nodes():
                species[node] = self.structure[node].specie.symbol
                coords[node] = self.structure[node].coords
                properties[node] = self.structure[node].properties

            nx.set_node_attributes(self.graph, species, "specie")
            nx.set_node_attributes(self.graph, coords, "coords")
            nx.set_node_attributes(self.graph, properties, "properties")

        def alter_edge(self, from_index, to_index, to_jimage=None,
                       new_weight=None, new_edge_properties=None):
            """
            Alters either the weight or the edge_properties of
            an edge in the StructureGraph.

            :param from_index: int
            :param to_index: int
            :param to_jimage: tuple
            :param new_weight: alter_edge does not require
                that weight be altered. As such, by default, this
                is None. If weight is to be changed, it should be a
                float.
            :param new_edge_properties: alter_edge does not require
                that edge_properties be altered. As such, by default,
                this is None. If any edge properties are to be changed,
                it should be a dictionary of edge properties to be changed.
            :return:
            """

            existing_edges = self.graph.get_edge_data(from_index, to_index)

            # ensure that edge exists before attempting to change it
            if not existing_edges:
                raise ValueError("Edge between {} and {} cannot be altered;\
                                    no edge exists between those sites.".format(
                    from_index, to_index
                ))

            if to_jimage is None:
                edge_index = 0
            else:
                for i, properties in existing_edges.items():
                    if properties["to_jimage"] == to_jimage:
                        edge_index = i

            if new_weight is not None:
                self.graph[from_index][to_index][edge_index]['weight'] = new_weight

            if new_edge_properties is not None:
                for prop in list(new_edge_properties.keys()):
                    self.graph[from_index][to_index][edge_index][prop] = new_edge_properties[prop]

        def break_edge(self, from_index, to_index, to_jimage=None, allow_reverse=False):
            """
            Remove an edge from the StructureGraph. If no image is given, this method will fail.

            :param from_index: int
            :param to_index: int
            :param to_jimage: tuple
            :param allow_reverse: If allow_reverse is True, then break_edge will
                attempt to break both (from_index, to_index) and, failing that,
                will attempt to break (to_index, from_index).
            :return:
            """

            # ensure that edge exists before attempting to remove it
            existing_edges = self.graph.get_edge_data(from_index, to_index)
            existing_reverse = None

            if to_jimage is None:
                raise ValueError("Image must be supplied, to avoid ambiguity.")

            if existing_edges:
                for i, properties in existing_edges.items():
                    if properties["to_jimage"] == to_jimage:
                        edge_index = i

                self.graph.remove_edge(from_index, to_index, edge_index)

            else:
                if allow_reverse:
                    existing_reverse = self.graph.get_edge_data(to_index, from_index)

                if existing_reverse:
                    for i, properties in existing_reverse.items():
                        if properties["to_jimage"] == to_jimage:
                            edge_index = i

                    self.graph.remove_edge(to_index, from_index, edge_index)
                else:
                    raise ValueError("Edge cannot be broken between {} and {};\
                                    no edge exists between those sites.".format(
                        from_index, to_index
                    ))

        def remove_nodes(self, indices):
            """
            A wrapper for Molecule.remove_sites().

            :param indices: list of indices in the current Molecule (and graph) to
                be removed.
            :return:
            """

            self.structure.remove_sites(indices)
            self.graph.remove_nodes_from(indices)

            mapping = {}
            for correct, current in enumerate(sorted(self.graph.nodes)):
                mapping[current] = correct

            nx.relabel_nodes(self.graph, mapping, copy=False)
            self.set_node_attributes()

        def substitute_group(self, index, func_grp, strategy, bond_order=1,
                             graph_dict=None, strategy_params=None):
            """
            Builds off of Structure.substitute to replace an atom in self.structure
            with a functional group. This method also amends self.graph to
            incorporate the new functional group.

            NOTE: Care must be taken to ensure that the functional group that is
            substituted will not place atoms to close to each other, or violate the
            dimensions of the Lattice.

            :param index: Index of atom to substitute.
            :param func_grp: Substituent molecule. There are two options:

                1. Providing an actual Molecule as the input. The first atom
                    must be a DummySpecie X, indicating the position of
                    nearest neighbor. The second atom must be the next
                    nearest atom. For example, for a methyl group
                    substitution, func_grp should be X-CH3, where X is the
                    first site and C is the second site. What the code will
                    do is to remove the index site, and connect the nearest
                    neighbor to the C atom in CH3. The X-C bond indicates the
                    directionality to connect the atoms.
                2. A string name. The molecule will be obtained from the
                    relevant template in func_groups.json.
            :param strategy: Class from pymatgen.analysis.local_env.
            :param bond_order: A specified bond order to calculate the bond
                length between the attached functional group and the nearest
                neighbor site. Defaults to 1.
            :param graph_dict: Dictionary representing the bonds of the functional
                group (format: {(u, v): props}, where props is a dictionary of
                properties, including weight. If None, then the algorithm
                will attempt to automatically determine bonds using one of
                a list of strategies defined in pymatgen.analysis.local_env.
            :param strategy_params: dictionary of keyword arguments for strategy.
                If None, default parameters will be used.
            :return:
            """

            def map_indices(grp):
                grp_map = {}

                # Get indices now occupied by functional group
                # Subtracting 1 because the dummy atom X should not count
                atoms = len(grp) - 1
                offset = len(self.structure) - atoms

                for i in range(atoms):
                    grp_map[i] = i + offset

                return grp_map

            if isinstance(func_grp, Molecule):
                func_grp = copy.deepcopy(func_grp)
            else:
                try:
                    func_grp = copy.deepcopy(FunctionalGroups[func_grp])
                except Exception:
                    raise RuntimeError("Can't find functional group in list. "
                                       "Provide explicit coordinate instead")

            self.structure.substitute(index, func_grp, bond_order=bond_order)

            mapping = map_indices(func_grp)

            # Remove dummy atom "X"
            func_grp.remove_species("X")

            if graph_dict is not None:
                for (u, v) in graph_dict.keys():
                    edge_props = graph_dict[(u, v)]
                    if "to_jimage" in edge_props.keys():
                        to_jimage = edge_props["to_jimage"]
                        del edge_props["to_jimage"]
                    else:
                        # By default, assume that all edges should stay remain
                        # inside the initial image
                        to_jimage = (0, 0, 0)
                    if "weight" in edge_props.keys():
                        weight = edge_props["weight"]
                        del edge_props["weight"]
                    self.add_edge(mapping[u], mapping[v], to_jimage=to_jimage,
                                  weight=weight, edge_properties=edge_props)

            else:
                if strategy_params is None:
                    strategy_params = {}
                strat = strategy(**strategy_params)

                for site in mapping.values():
                    neighbors = strat.get_nn_info(self.structure, site)

                    for neighbor in neighbors:
                        self.add_edge(from_index=site,
                                      from_jimage=(0, 0, 0),
                                      to_index=neighbor['site_index'],
                                      to_jimage=neighbor['image'],
                                      weight=neighbor['weight'],
                                      warn_duplicates=False)

        def get_connected_sites(self, n, jimage=(0, 0, 0)):
            """
            Returns a named tuple of neighbors of site n:
            periodic_site, jimage, index, weight.
            Index is the index of the corresponding site
            in the original structure, weight can be
            None if not defined.
            :param n: index of Site in Structure
            :param jimage: lattice vector of site
            :return: list of ConnectedSite tuples,
                sorted by closest first
            """

            connected_sites = set()
            connected_site_images = set()

            out_edges = [(u, v, d, 'out') for u, v, d in self.graph.out_edges(n, data=True)]
            in_edges = [(u, v, d, 'in') for u, v, d in self.graph.in_edges(n, data=True)]

            for u, v, d, dir in out_edges + in_edges:

                to_jimage = d['to_jimage']

                if dir == 'in':
                    u, v = v, u
                    to_jimage = np.multiply(-1, to_jimage)

                to_jimage = tuple(map(int, np.add(to_jimage, jimage)))
                site_d = self.structure[v].as_dict()
                site_d['abc'] = np.add(site_d['abc'], to_jimage).tolist()
                site = PeriodicSite.from_dict(site_d)

                # from_site if jimage arg != (0, 0, 0)
                relative_jimage = np.subtract(to_jimage, jimage)
                dist = self.structure[u].distance(self.structure[v], jimage=relative_jimage)

                weight = d.get('weight', None)

                if (v, to_jimage) not in connected_site_images:
                    connected_site = ConnectedSite(site=site,
                                                   jimage=to_jimage,
                                                   index=v,
                                                   weight=weight,
                                                   dist=dist)

                    connected_sites.add(connected_site)
                    connected_site_images.add((v, to_jimage))

            # return list sorted by closest sites first
            connected_sites = list(connected_sites)
            connected_sites.sort(key=lambda x: x.dist)

            return connected_sites

        def get_coordination_of_site(self, n):
            """
            Returns the number of neighbors of site n.
            In graph terms, simply returns degree
            of node corresponding to site n.
            :param n: index of site
            :return (int):
            """
            number_of_self_loops = sum([1 for n, v in self.graph.edges(n) if n == v])
            return self.graph.degree(n) - number_of_self_loops

        def draw_graph_to_file(self, filename="graph",
                               diff=None,
                               hide_unconnected_nodes=False,
                               hide_image_edges=True,
                               edge_colors=False,
                               node_labels=False,
                               weight_labels=False,
                               image_labels=False,
                               color_scheme="VESTA",
                               keep_dot=False,
                               algo="fdp"):
            """
            Draws graph using GraphViz.

            The networkx graph object itself can also be drawn
            with networkx's in-built graph drawing methods, but
            note that this might give misleading results for
            multigraphs (edges are super-imposed on each other).

            If visualization is difficult to interpret,
            `hide_image_edges` can help, especially in larger
            graphs.

            :param filename: filename to output, will detect filetype
                from extension (any graphviz filetype supported, such as
                pdf or png)
            :param diff (StructureGraph): an additional graph to
                compare with, will color edges red that do not exist in diff
                and edges green that are in diff graph but not in the
                reference graph
            :param hide_unconnected_nodes: if True, hide unconnected
                nodes
            :param hide_image_edges: if True, do not draw edges that
                go through periodic boundaries
            :param edge_colors (bool): if True, use node colors to
                color edges
            :param node_labels (bool): if True, label nodes with
                species and site index
            :param weight_labels (bool): if True, label edges with
                weights
            :param image_labels (bool): if True, label edges with
                their periodic images (usually only used for debugging,
                edges to periodic images always appear as dashed lines)
            :param color_scheme (str): "VESTA" or "JMOL"
            :param keep_dot (bool): keep GraphViz .dot file for later
                visualization
            :param algo: any graphviz algo, "neato" (for simple graphs)
                or "fdp" (for more crowded graphs) usually give good outputs
            :return:
            """

            if not which(algo):
                raise RuntimeError("StructureGraph graph drawing requires "
                                   "GraphViz binaries to be in the path.")

            # Developer note: NetworkX also has methods for drawing
            # graphs using matplotlib, these also work here. However,
            # a dedicated tool like GraphViz allows for much easier
            # control over graph appearance and also correctly displays
            # mutli-graphs (matplotlib can superimpose multiple edges).

            g = self.graph.copy()

            g.graph = {'nodesep': 10.0, 'dpi': 300, 'overlap': "false"}

            # add display options for nodes
            for n in g.nodes():
                # get label by species name
                label = "{}({})".format(str(self.structure[n].specie), n) if node_labels else ""

                # use standard color scheme for nodes
                c = EL_COLORS[color_scheme].get(str(self.structure[n].specie.symbol), [0, 0, 0])

                # get contrasting font color
                # magic numbers account for perceived luminescence
                # https://stackoverflow.com/questions/1855884/determine-font-color-based-on-background-color
                fontcolor = '#000000' if 1 - (c[0] * 0.299 + c[1] * 0.587
                                              + c[2] * 0.114) / 255 < 0.5 else '#ffffff'

                # convert color to hex string
                color = "#{:02x}{:02x}{:02x}".format(c[0], c[1], c[2])

                g.add_node(n, fillcolor=color, fontcolor=fontcolor, label=label,
                           fontname="Helvetica-bold", style="filled", shape="circle")

            edges_to_delete = []

            # add display options for edges
            for u, v, k, d in g.edges(keys=True, data=True):

                # retrieve from/to images, set as origin if not defined
                to_image = d['to_jimage']

                # set edge style
                d['style'] = "solid"
                if to_image != (0, 0, 0):
                    d['style'] = "dashed"
                    if hide_image_edges:
                        edges_to_delete.append((u, v, k))

                # don't show edge directions
                d['arrowhead'] = "none"

                # only add labels for images that are not the origin
                if image_labels:
                    d['headlabel'] = "" if to_image == (0, 0, 0) else "to {}".format((to_image))
                    d['arrowhead'] = "normal" if d['headlabel'] else "none"

                # optionally color edges using node colors
                color_u = g.nodes[u]['fillcolor']
                color_v = g.nodes[v]['fillcolor']
                d['color_uv'] = "{};0.5:{};0.5".format(color_u, color_v) if edge_colors else "#000000"

                # optionally add weights to graph
                if weight_labels:
                    units = g.graph.get('edge_weight_units', "")
                    if d.get('weight'):
                        d['label'] = "{:.2f} {}".format(d['weight'], units)

                # update edge with our new style attributes
                g.edges[u, v, k].update(d)

            # optionally remove periodic image edges,
            # these can be confusing due to periodic boundaries
            if hide_image_edges:
                for edge_to_delete in edges_to_delete:
                    g.remove_edge(*edge_to_delete)

            # optionally hide unconnected nodes,
            # these can appear when removing periodic edges
            if hide_unconnected_nodes:
                g = g.subgraph([n for n in g.degree() if g.degree()[n] != 0])

            # optionally highlight differences with another graph
            if diff:
                diff = self.diff(diff, strict=True)
                green_edges = []
                red_edges = []
                for u, v, k, d in g.edges(keys=True, data=True):
                    if (u, v, d['to_jimage']) in diff['self']:
                        # edge has been deleted
                        red_edges.append((u, v, k))
                    elif (u, v, d['to_jimage']) in diff['other']:
                        # edge has been added
                        green_edges.append((u, v, k))
                for u, v, k in green_edges:
                    g.edges[u, v, k].update({'color_uv': '#00ff00'})
                for u, v, k in red_edges:
                    g.edges[u, v, k].update({'color_uv': '#ff0000'})

            basename, extension = os.path.splitext(filename)
            extension = extension[1:]

            write_dot(g, basename + ".dot")

            with open(filename, "w") as f:

                args = [algo, "-T", extension, basename + ".dot"]
                rs = subprocess.Popen(args,
                                      stdout=f,
                                      stdin=subprocess.PIPE, close_fds=True)
                rs.communicate()
                if rs.returncode != 0:
                    raise RuntimeError("{} exited with return code {}.".format(algo, rs.returncode))

            if not keep_dot:
                os.remove(basename + ".dot")

        @property
        def types_and_weights_of_connections(self):
            """
            Extract a dictionary summarizing the types and weights
            of edges in the graph.

            :return: A dictionary with keys specifying the
                species involved in a connection in alphabetical order
                (e.g. string 'Fe-O') and values which are a list of
                weights for those connections (e.g. bond lengths).
            """

            def get_label(u, v):
                u_label = self.structure[u].species_string
                v_label = self.structure[v].species_string
                return "-".join(sorted((u_label, v_label)))

            types = defaultdict(list)
            for u, v, d in self.graph.edges(data=True):
                label = get_label(u, v)
                types[label].append(d['weight'])

            return dict(types)

        @property
        def weight_statistics(self):
            """
            Extract a statistical summary of edge weights present in
            the graph.

            :return: A dict with an 'all_weights' list, 'minimum',
                'maximum', 'median', 'mean', 'std_dev'
            """

            all_weights = [d.get('weight', None) for u, v, d
                           in self.graph.edges(data=True)]
            stats = describe(all_weights, nan_policy='omit')

            return {
                'all_weights': all_weights,
                'min': stats.minmax[0],
                'max': stats.minmax[1],
                'mean': stats.mean,
                'variance': stats.variance
            }

        def types_of_coordination_environments(self, anonymous=False):
            """
            Extract information on the different co-ordination environments
            present in the graph.

            :param anonymous: if anonymous, will replace specie names
                with A, B, C, etc.
            :return: a list of co-ordination environments,
                e.g. ['Mo-S(6)', 'S-Mo(3)']
            """

            motifs = set()
            for idx, site in enumerate(self.structure):

                centre_sp = site.species_string

                connected_sites = self.get_connected_sites(idx)
                connected_species = [connected_site.site.species_string
                                     for connected_site in connected_sites]

                labels = []
                for sp in set(connected_species):
                    count = connected_species.count(sp)
                    labels.append((count, sp))

                labels = sorted(labels, reverse=True)

                if anonymous:
                    mapping = {centre_sp: 'A'}
                    available_letters = [chr(66 + i) for i in range(25)]
                    for label in labels:
                        sp = label[1]
                        if sp not in mapping:
                            mapping[sp] = available_letters.pop(0)
                    centre_sp = 'A'
                    labels = [(label[0], mapping[label[1]]) for label in labels]

                labels = ["{}({})".format(label[1], label[0]) for label in labels]
                motif = '{}-{}'.format(centre_sp, ','.join(labels))
                motifs.add(motif)

            return sorted(list(motifs))

        def as_dict(self):
            """
            As in :Class: `pymatgen.core.Structure` except
            with using `to_dict_of_dicts` from NetworkX
            to store graph information.
            """

            d = {"@module": self.__class__.__module__,
                 "@class": self.__class__.__name__,
                 "structure": self.structure.as_dict(),
                 "graphs": json_graph.adjacency_data(self.graph)}

            return d

        @classmethod
        def from_dict(cls, d):
            """
            As in :Class: `pymatgen.core.Structure` except
            restoring graphs using `from_dict_of_dicts`
            from NetworkX to restore graph information.
            """
            s = Structure.from_dict(d['structure'])
            return cls(s, d['graphs'])

        def __mul__(self, scaling_matrix):
            """
            Replicates the graph, creating a supercell,
            intelligently joining together
            edges that lie on periodic boundaries.
            In principle, any operations on the expanded
            graph could also be done on the original
            graph, but a larger graph can be easier to
            visualize and reason about.
            :param scaling_matrix: same as Structure.__mul__
            :return:
            """

            # Developer note: a different approach was also trialed, using
            # a simple Graph (instead of MultiDiGraph), with node indices
            # representing both site index and periodic image. Here, the
            # number of nodes != number of sites in the Structure. This
            # approach has many benefits, but made it more difficult to
            # keep the graph in sync with its corresponding Structure.

            # Broadly, it would be easier to multiply the Structure
            # *before* generating the StructureGraph, but this isn't
            # possible when generating the graph using critic2 from
            # charge density.

            # Multiplication works by looking for the expected position
            # of an image node, and seeing if that node exists in the
            # supercell. If it does, the edge is updated. This is more
            # computationally expensive than just keeping track of the
            # which new lattice images present, but should hopefully be
            # easier to extend to a general 3x3 scaling matrix.

            # code adapted from Structure.__mul__
            scale_matrix = np.array(scaling_matrix, np.int16)
            if scale_matrix.shape != (3, 3):
                scale_matrix = np.array(scale_matrix * np.eye(3), np.int16)
            else:
                # TODO: test __mul__ with full 3x3 scaling matrices
                raise NotImplementedError('Not tested with 3x3 scaling matrices yet.')
            new_lattice = Lattice(np.dot(scale_matrix, self.structure.lattice.matrix))

            f_lat = lattice_points_in_supercell(scale_matrix)
            c_lat = new_lattice.get_cartesian_coords(f_lat)

            new_sites = []
            new_graphs = []

            for v in c_lat:

                # create a map of nodes from original graph to its image
                mapping = {n: n + len(new_sites) for n in range(len(self.structure))}

                for idx, site in enumerate(self.structure):
                    s = PeriodicSite(site.species, site.coords + v,
                                     new_lattice, properties=site.properties,
                                     coords_are_cartesian=True, to_unit_cell=False)

                    new_sites.append(s)

                new_graphs.append(nx.relabel_nodes(self.graph, mapping, copy=True))

            new_structure = Structure.from_sites(new_sites)

            # merge all graphs into one big graph
            new_g = nx.MultiDiGraph()
            for new_graph in new_graphs:
                new_g = nx.union(new_g, new_graph)

            edges_to_remove = []  # tuple of (u, v, k)
            edges_to_add = []  # tuple of (u, v, attr_dict)

            # list of new edges inside supercell
            # for duplicate checking
            edges_inside_supercell = [{u, v} for u, v, d in new_g.edges(data=True)
                                      if d['to_jimage'] == (0, 0, 0)]
            new_periodic_images = []

            orig_lattice = self.structure.lattice

            # use k-d tree to match given position to an
            # existing Site in Structure
            kd_tree = KDTree(new_structure.cart_coords)

            # tolerance in Å for sites to be considered equal
            # this could probably be a lot smaller
            tol = 0.05

            for u, v, k, d in new_g.edges(keys=True, data=True):

                to_jimage = d['to_jimage']  # for node v

                # reduce unnecessary checking
                if to_jimage != (0, 0, 0):

                    # get index in original site
                    n_u = u % len(self.structure)
                    n_v = v % len(self.structure)

                    # get fractional co-ordinates of where atoms defined
                    # by edge are expected to be, relative to original
                    # lattice (keeping original lattice has
                    # significant benefits)
                    v_image_frac = np.add(self.structure[n_v].frac_coords, to_jimage)
                    u_frac = self.structure[n_u].frac_coords

                    # using the position of node u as a reference,
                    # get relative Cartesian co-ordinates of where
                    # atoms defined by edge are expected to be
                    v_image_cart = orig_lattice.get_cartesian_coords(v_image_frac)
                    u_cart = orig_lattice.get_cartesian_coords(u_frac)
                    v_rel = np.subtract(v_image_cart, u_cart)

                    # now retrieve position of node v in
                    # new supercell, and get asgolute Cartesian
                    # co-ordinates of where atoms defined by edge
                    # are expected to be
                    v_expec = new_structure[u].coords + v_rel

                    # now search in new structure for these atoms
                    # query returns (distance, index)
                    v_present = kd_tree.query(v_expec)
                    v_present = v_present[1] if v_present[0] <= tol else None

                    # check if image sites now present in supercell
                    # and if so, delete old edge that went through
                    # periodic boundary
                    if v_present is not None:

                        new_u = u
                        new_v = v_present
                        new_d = d.copy()

                        # node now inside supercell
                        new_d['to_jimage'] = (0, 0, 0)

                        edges_to_remove.append((u, v, k))

                        # make sure we don't try to add duplicate edges
                        # will remove two edges for everyone one we add
                        if {new_u, new_v} not in edges_inside_supercell:

                            # normalize direction
                            if new_v < new_u:
                                new_u, new_v = new_v, new_u

                            edges_inside_supercell.append({new_u, new_v})
                            edges_to_add.append((new_u, new_v, new_d))

                    else:

                        # want to find new_v such that we have
                        # full periodic boundary conditions
                        # so that nodes on one side of supercell
                        # are connected to nodes on opposite side

                        v_expec_frac = new_structure.lattice.get_fractional_coords(v_expec)

                        # find new to_jimage
                        # use np.around to fix issues with finite precision leading to incorrect image
                        v_expec_image = np.around(v_expec_frac, decimals=3)
                        v_expec_image = v_expec_image - v_expec_image % 1

                        v_expec_frac = np.subtract(v_expec_frac, v_expec_image)
                        v_expec = new_structure.lattice.get_cartesian_coords(v_expec_frac)
                        v_present = kd_tree.query(v_expec)
                        v_present = v_present[1] if v_present[0] <= tol else None

                        if v_present is not None:

                            new_u = u
                            new_v = v_present
                            new_d = d.copy()
                            new_to_jimage = tuple(map(int, v_expec_image))

                            # normalize direction
                            if new_v < new_u:
                                new_u, new_v = new_v, new_u
                                new_to_jimage = tuple(np.multiply(-1, d['to_jimage']).astype(int))

                            new_d['to_jimage'] = new_to_jimage

                            edges_to_remove.append((u, v, k))

                            if (new_u, new_v, new_to_jimage) not in new_periodic_images:
                                edges_to_add.append((new_u, new_v, new_d))
                                new_periodic_images.append((new_u, new_v, new_to_jimage))

            logger.debug("Removing {} edges, adding {} new edges.".format(len(edges_to_remove),
                                                                          len(edges_to_add)))

            # add/delete marked edges
            for edges_to_remove in edges_to_remove:
                new_g.remove_edge(*edges_to_remove)
            for (u, v, d) in edges_to_add:
                new_g.add_edge(u, v, **d)

            # return new instance of StructureGraph with supercell
            d = {"@module": self.__class__.__module__,
                 "@class": self.__class__.__name__,
                 "structure": new_structure.as_dict(),
                 "graphs": json_graph.adjacency_data(new_g)}

            sg = StructureGraph.from_dict(d)

            return sg

        def __rmul__(self, other):
            return self.__mul__(other)

        def _edges_to_string(self, g):

            header = "from    to  to_image    "
            header_line = "----  ----  ------------"
            edge_weight_name = g.graph["edge_weight_name"]
            if edge_weight_name:
                print_weights = ["weight"]
                edge_label = g.graph["edge_weight_name"]
                edge_weight_units = g.graph["edge_weight_units"]
                if edge_weight_units:
                    edge_label += " ({})".format(edge_weight_units)
                header += "  {}".format(edge_label)
                header_line += "  {}".format("-" * max([18, len(edge_label)]))
            else:
                print_weights = False

            s = header + "\n" + header_line + "\n"

            edges = list(g.edges(data=True))

            # sort edges for consistent ordering
            edges.sort(key=itemgetter(0, 1))

            if print_weights:
                for u, v, data in edges:
                    s += "{:4}  {:4}  {:12}  {:.3e}\n".format(u, v, str(data.get("to_jimage", (0, 0, 0))),
                                                              data.get("weight", 0))
            else:
                for u, v, data in edges:
                    s += "{:4}  {:4}  {:12}\n".format(u, v,
                                                      str(data.get("to_jimage", (0, 0, 0))))

            return s

        def __str__(self):
            s = "Structure Graph"
            s += "\nStructure: \n{}".format(self.structure.__str__())
            s += "\nGraph: {}\n".format(self.name)
            s += self._edges_to_string(self.graph)
            return s

        def __repr__(self):
            s = "Structure Graph"
            s += "\nStructure: \n{}".format(self.structure.__repr__())
            s += "\nGraph: {}\n".format(self.name)
            s += self._edges_to_string(self.graph)
            return s

        def __len__(self):
            """
            :return: length of Structure / number of nodes in graph
            """
            return len(self.structure)

        def sort(self, key=None, reverse=False):
            """
            Same as Structure.sort(), also remaps nodes in graph.
            :param key:
            :param reverse:
            :return:
            """

            old_structure = self.structure.copy()

            # sort Structure
            self.structure._sites = sorted(self.structure._sites, key=key, reverse=reverse)

            # apply Structure ordering to graph
            mapping = {idx: self.structure.index(site) for idx, site in enumerate(old_structure)}
            self.graph = nx.relabel_nodes(self.graph, mapping, copy=True)

            # normalize directions of edges
            edges_to_remove = []
            edges_to_add = []
            for u, v, k, d in self.graph.edges(keys=True, data=True):
                if v < u:
                    new_v, new_u, new_d = u, v, d.copy()
                    new_d['to_jimage'] = tuple(np.multiply(-1, d['to_jimage']).astype(int))
                    edges_to_remove.append((u, v, k))
                    edges_to_add.append((new_u, new_v, new_d))

            # add/delete marked edges
            for edges_to_remove in edges_to_remove:
                self.graph.remove_edge(*edges_to_remove)
            for (u, v, d) in edges_to_add:
                self.graph.add_edge(u, v, **d)

        def __copy__(self):
            return StructureGraph.from_dict(self.as_dict())

        def __eq__(self, other):
            """
            Two StructureGraphs are equal if they have equal Structures,
            and have the same edges between Sites. Edge weights can be
            different and StructureGraphs can still be considered equal.

            :param other: StructureGraph
            :return (bool):
            """

            # sort for consistent node indices
            # PeriodicSite should have a proper __hash__() value,
            # using its frac_coords as a convenient key
            mapping = {tuple(site.frac_coords): self.structure.index(site) for site in other.structure}
            other_sorted = other.__copy__()
            other_sorted.sort(key=lambda site: mapping[tuple(site.frac_coords)])

            edges = {(u, v, d['to_jimage'])
                     for u, v, d in self.graph.edges(keys=False, data=True)}

            edges_other = {(u, v, d['to_jimage'])
                           for u, v, d in other_sorted.graph.edges(keys=False, data=True)}

            return (edges == edges_other) and \
                   (self.structure == other_sorted.structure)

        def diff(self, other, strict=True):
            """
            Compares two StructureGraphs. Returns dict with
            keys 'self', 'other', 'both' with edges that are
            present in only one StructureGraph ('self' and
            'other'), and edges that are present in both.

            The Jaccard distance is a simple measure of the
            dissimilarity between two StructureGraphs (ignoring
            edge weights), and is defined by 1 - (size of the
            intersection / size of the union) of the sets of
            edges. This is returned with key 'dist'.

            Important note: all node indices are in terms
            of the StructureGraph this method is called
            from, not the 'other' StructureGraph: there
            is no guarantee the node indices will be the
            same if the underlying Structures are ordered
            differently.

            :param other: StructureGraph
            :param strict: if False, will compare bonds
                from different Structures, with node indices
                replaced by Specie strings, will not count
                number of occurrences of bonds
            :return:
            """

            if self.structure != other.structure and strict:
                return ValueError("Meaningless to compare StructureGraphs if "
                                  "corresponding Structures are different.")

            if strict:

                # sort for consistent node indices
                # PeriodicSite should have a proper __hash__() value,
                # using its frac_coords as a convenient key
                mapping = {tuple(site.frac_coords): self.structure.index(site) for site in other.structure}
                other_sorted = other.__copy__()
                other_sorted.sort(key=lambda site: mapping[tuple(site.frac_coords)])

                edges = {(u, v, d['to_jimage'])
                         for u, v, d in self.graph.edges(keys=False, data=True)}

                edges_other = {(u, v, d['to_jimage'])
                               for u, v, d in other_sorted.graph.edges(keys=False, data=True)}

            else:

                edges = {(str(self.structure[u].specie),
                          str(self.structure[v].specie))
                         for u, v, d in self.graph.edges(keys=False, data=True)}

                edges_other = {(str(other.structure[u].specie),
                                str(other.structure[v].specie))
                               for u, v, d in other.graph.edges(keys=False, data=True)}

            if len(edges) == 0 and len(edges_other) == 0:
                jaccard_dist = 0  # by definition
            else:
                jaccard_dist = 1 - len(edges.intersection(edges_other)) / len(edges.union(edges_other))

            return {
                'self': edges - edges_other,
                'other': edges_other - edges,
                'both': edges.intersection(edges_other),
                'dist': jaccard_dist
            }

        def get_subgraphs_as_molecules(self, use_weights=False):
            """
            Retrieve subgraphs as molecules, useful for extracting
            molecules from periodic crystals.

            Will only return unique molecules, not any duplicates
            present in the crystal (a duplicate defined as an
            isomorphic subgraph).

            :param use_weights (bool): If True, only treat subgraphs
                as isomorphic if edges have the same weights. Typically,
                this means molecules will need to have the same bond
                lengths to be defined as duplicates, otherwise bond
                lengths can differ. This is a fairly robust approach,
                but will treat e.g. enantiomers as being duplicates.

            :return: list of unique Molecules in Structure
            """

            # creating a supercell is an easy way to extract
            # molecules (and not, e.g., layers of a 2D crystal)
            # without adding extra logic
            if getattr(self, '_supercell_sg', None) is None:
                self._supercell_sg = supercell_sg = self * (3, 3, 3)

            # make undirected to find connected subgraphs
            supercell_sg.graph = nx.Graph(supercell_sg.graph)

            # find subgraphs
            all_subgraphs = [supercell_sg.graph.subgraph(c) for c in
                             nx.connected_components(supercell_sg.graph)]

            # discount subgraphs that lie across *supercell* boundaries
            # these will subgraphs representing crystals
            molecule_subgraphs = []
            for subgraph in all_subgraphs:
                intersects_boundary = any([d['to_jimage'] != (0, 0, 0)
                                           for u, v, d in subgraph.edges(data=True)])
                if not intersects_boundary:
                    molecule_subgraphs.append(nx.MultiDiGraph(subgraph))

            # add specie names to graph to be able to test for isomorphism
            for subgraph in molecule_subgraphs:
                for n in subgraph:
                    subgraph.add_node(n, specie=str(supercell_sg.structure[n].specie))

            # now define how we test for isomorphism
            def node_match(n1, n2):
                return n1['specie'] == n2['specie']

            def edge_match(e1, e2):
                if use_weights:
                    return e1['weight'] == e2['weight']
                else:
                    return True

            # prune duplicate subgraphs
            unique_subgraphs = []
            for subgraph in molecule_subgraphs:

                already_present = [nx.is_isomorphic(subgraph, g,
                                                    node_match=node_match,
                                                    edge_match=edge_match)
                                   for g in unique_subgraphs]

                if not any(already_present):
                    unique_subgraphs.append(subgraph)

            # get Molecule objects for each subgraph
            molecules = []
            for subgraph in unique_subgraphs:
                coords = [supercell_sg.structure[n].coords for n
                          in subgraph.nodes()]
                species = [supercell_sg.structure[n].specie for n
                           in subgraph.nodes()]

                molecule = Molecule(species, coords)

                # shift so origin is at center of mass
                molecule = molecule.get_centered_molecule()

                molecules.append(molecule)

            return molecules

    class MolGraphSplitError(Exception):
        """
        Raised when a molecule graph is failed to split into two disconnected
        subgraphs
        """
        pass

    class MoleculeGraph(MSONable):
        """
        This is a class for annotating a Molecule with
        bond information, stored in the form of a graph. A "bond" does
        not necessarily have to be a chemical bond, but can store any
        kind of information that connects two Sites.
        """

        def __init__(self, molecule, graph_data=None):
            """
            If constructing this class manually, use the `with_empty_graph`
            method or `with_local_env_strategy` method (using an algorithm
            provided by the `local_env` module, such as O'Keeffe).

            This class that contains connection information:
            relationships between sites represented by a Graph structure,
            and an associated structure object.

            This class uses the NetworkX package to store and operate
            on the graph itself, but contains a lot of helper methods
            to make associating a graph with a given molecule easier.

            Use cases for this include storing bonding information,
            NMR J-couplings, Heisenberg exchange parameters, etc.

            :param molecule: Molecule object

            :param graph_data: dict containing graph information in
                dict format (not intended to be constructed manually,
                see as_dict method for format)
            """

            if isinstance(molecule, MoleculeGraph):
                # just make a copy from input
                graph_data = molecule.as_dict()['graphs']

            self.molecule = molecule
            self.graph = nx.readwrite.json_graph.adjacency_graph(graph_data)

            # tidy up edge attr dicts, reading to/from json duplicates
            # information
            for u, v, k, d in self.graph.edges(keys=True, data=True):
                if 'id' in d:
                    del d['id']
                if 'key' in d:
                    del d['key']
                # ensure images are tuples (conversion to lists happens
                # when serializing back from json), it's important images
                # are hashable/immutable
                if 'to_jimage' in d:
                    d['to_jimage'] = tuple(d['to_jimage'])
                if 'from_jimage' in d:
                    d['from_jimage'] = tuple(d['from_jimage'])

            self.set_node_attributes()

        @classmethod
        def with_empty_graph(cls, molecule, name="bonds",
                             edge_weight_name=None,
                             edge_weight_units=None):
            """
            Constructor for MoleculeGraph, returns a MoleculeGraph
            object with an empty graph (no edges, only nodes defined
            that correspond to Sites in Molecule).

            :param molecule (Molecule):
            :param name (str): name of graph, e.g. "bonds"
            :param edge_weight_name (str): name of edge weights,
                e.g. "bond_length" or "exchange_constant"
            :param edge_weight_units (str): name of edge weight units
                e.g. "Å" or "eV"
            :return (MoleculeGraph):
            """

            if edge_weight_name and (edge_weight_units is None):
                raise ValueError("Please specify units associated "
                                 "with your edge weights. Can be "
                                 "empty string if arbitrary or "
                                 "dimensionless.")

            # construct graph with one node per site
            # graph attributes don't change behavior of graph,
            # they're just for book-keeping
            graph = nx.MultiDiGraph(edge_weight_name=edge_weight_name,
                                    edge_weight_units=edge_weight_units,
                                    name=name)
            graph.add_nodes_from(range(len(molecule)))

            graph_data = json_graph.adjacency_data(graph)

            return cls(molecule, graph_data=graph_data)

        @staticmethod
        def with_edges(molecule, edges):
            """
            Constructor for MoleculeGraph, using pre-existing or pre-defined edges
            with optional edge parameters.

            :param molecule: Molecule object
            :param edges: dict representing the bonds of the functional
                group (format: {(u, v): props}, where props is a dictionary of
                properties, including weight. Props should be None if no
                additional properties are to be specified.
            :return: mg, a MoleculeGraph
            """

            mg = MoleculeGraph.with_empty_graph(molecule, name="bonds",
                                                edge_weight_name="weight",
                                                edge_weight_units="")

            for edge, props in edges.items():

                try:
                    from_index = edge[0]
                    to_index = edge[1]
                except TypeError:
                    raise ValueError("Edges must be given as (from_index, to_index)"
                                     "tuples")

                if props is not None:
                    if "weight" in props.keys():
                        weight = props["weight"]
                        del props["weight"]
                    else:
                        weight = None

                    if len(props.items()) == 0:
                        props = None
                else:
                    weight = None

                nodes = mg.graph.nodes
                if not (from_index in nodes and to_index in nodes):
                    raise ValueError("Edges cannot be added if nodes are not"
                                     " present in the graph. Please check your"
                                     " indices.")

                mg.add_edge(from_index, to_index, weight=weight,
                            edge_properties=props)

            mg.set_node_attributes()
            return mg

        @staticmethod
        def with_local_env_strategy(molecule, strategy):
            """
            Constructor for MoleculeGraph, using a strategy
            from :Class: `pymatgen.analysis.local_env`.

            :param molecule: Molecule object
            :param strategy: an instance of a
                :Class: `pymatgen.analysis.local_env.NearNeighbors` object
            :return: mg, a MoleculeGraph
            """

            if not strategy.molecules_allowed:
                raise ValueError("Chosen strategy is not designed for use with molecules! "
                                 "Please choose another strategy.")
            if strategy.extend_structure_molecules:
                extend_structure = True
            else:
                extend_structure = False

            mg = MoleculeGraph.with_empty_graph(molecule, name="bonds",
                                                edge_weight_name="weight",
                                                edge_weight_units="")

            # NearNeighbor classes only (generally) work with structures
            # molecules have to be boxed first
            coords = molecule.cart_coords

            if extend_structure:
                a = max(coords[:, 0]) - min(coords[:, 0]) + 100
                b = max(coords[:, 1]) - min(coords[:, 1]) + 100
                c = max(coords[:, 2]) - min(coords[:, 2]) + 100

                structure = molecule.get_boxed_structure(a, b, c, no_cross=True,
                                                         reorder=False)
            else:
                structure = None

            for n in range(len(molecule)):

                if structure is None:
                    neighbors = strategy.get_nn_info(molecule, n)
                else:
                    neighbors = strategy.get_nn_info(structure, n)
                for neighbor in neighbors:

                    # all bonds in molecules should not cross
                    # (artificial) periodic boundaries
                    if not np.array_equal(neighbor['image'], [0, 0, 0]):
                        continue

                    if n > neighbor['site_index']:
                        from_index = neighbor['site_index']
                        to_index = n
                    else:
                        from_index = n
                        to_index = neighbor['site_index']

                    mg.add_edge(from_index=from_index,
                                to_index=to_index,
                                weight=neighbor['weight'],
                                warn_duplicates=False)

            duplicates = []
            for edge in mg.graph.edges:
                if edge[2] != 0:
                    duplicates.append(edge)

            for duplicate in duplicates:
                mg.graph.remove_edge(duplicate[0], duplicate[1], key=duplicate[2])

            mg.set_node_attributes()
            return mg

        @property
        def name(self):
            """
            :return: Name of graph
            """
            return self.graph.graph['name']

        @property
        def edge_weight_name(self):
            """
            :return: Name of the edge weight property of graph
            """
            return self.graph.graph['edge_weight_name']

        @property
        def edge_weight_unit(self):
            """
            :return: Units of the edge weight property of graph
            """
            return self.graph.graph['edge_weight_units']

        def add_edge(self, from_index, to_index,
                     weight=None, warn_duplicates=True,
                     edge_properties=None):
            """
            Add edge to graph.

            Since physically a 'bond' (or other connection
            between sites) doesn't have a direction, from_index,
            from_jimage can be swapped with to_index, to_jimage.

            However, images will always always be shifted so that
            from_index < to_index and from_jimage becomes (0, 0, 0).

            :param from_index: index of site connecting from
            :param to_index: index of site connecting to
            :param weight (float): e.g. bond length
            :param warn_duplicates (bool): if True, will warn if
                trying to add duplicate edges (duplicate edges will not
                be added in either case)
            :param edge_properties (dict): any other information to
                store on graph edges, similar to Structure's site_properties
            :return:
            """

            # this is not necessary for the class to work, but
            # just makes it neater
            if to_index < from_index:
                to_index, from_index = from_index, to_index

            # sanitize types
            from_index, to_index = int(from_index), int(to_index)

            # check we're not trying to add a duplicate edge
            # there should only ever be at most one edge
            # between two sites
            existing_edge_data = self.graph.get_edge_data(from_index, to_index)
            if existing_edge_data and warn_duplicates:
                warnings.warn("Trying to add an edge that already exists from "
                              "site {} to site {}.".format(from_index,
                                                           to_index))
                return

            # generic container for additional edge properties,
            # similar to site properties
            edge_properties = edge_properties or {}

            if weight:
                self.graph.add_edge(from_index, to_index,
                                    weight=weight,
                                    **edge_properties)
            else:
                self.graph.add_edge(from_index, to_index,
                                    **edge_properties)

        def insert_node(self, i, species, coords, validate_proximity=False,
                        site_properties=None, edges=None):
            """
            A wrapper around Molecule.insert(), which also incorporates the new
            site into the MoleculeGraph.

            :param i: Index at which to insert the new site
            :param species: Species for the new site
            :param coords: 3x1 array representing coordinates of the new site
            :param validate_proximity: For Molecule.insert(); if True (default
                False), distance will be checked to ensure that site can be safely
                added.
            :param site_properties: Site properties for Molecule
            :param edges: List of dicts representing edges to be added to the
                MoleculeGraph. These edges must include the index of the new site i,
                and all indices used for these edges should reflect the
                MoleculeGraph AFTER the insertion, NOT before. Each dict should at
                least have a "to_index" and "from_index" key, and can also have a
                "weight" and a "properties" key.
            :return:
            """

            self.molecule.insert(i, species, coords,
                                 validate_proximity=validate_proximity,
                                 properties=site_properties)

            mapping = {}
            for j in range(len(self.molecule) - 1):
                if j < i:
                    mapping[j] = j
                else:
                    mapping[j] = j + 1
            nx.relabel_nodes(self.graph, mapping, copy=False)

            self.graph.add_node(i)
            self.set_node_attributes()

            if edges is not None:
                for edge in edges:
                    try:
                        self.add_edge(edge["from_index"], edge["to_index"],
                                      weight=edge.get("weight", None),
                                      edge_properties=edge.get("properties", None))
                    except KeyError:
                        raise RuntimeError("Some edges are invalid.")

        def set_node_attributes(self):
            """
            Replicates molecule site properties (specie, coords, etc.) in the
            MoleculeGraph.

            :return:
            """

            species = {}
            coords = {}
            properties = {}
            for node in self.graph.nodes():
                species[node] = self.molecule[node].specie.symbol
                coords[node] = self.molecule[node].coords
                properties[node] = self.molecule[node].properties

            nx.set_node_attributes(self.graph, species, "specie")
            nx.set_node_attributes(self.graph, coords, "coords")
            nx.set_node_attributes(self.graph, properties, "properties")

        def alter_edge(self, from_index, to_index,
                       new_weight=None, new_edge_properties=None):
            """
            Alters either the weight or the edge_properties of
            an edge in the MoleculeGraph.

            :param from_index: int
            :param to_index: int
            :param new_weight: alter_edge does not require
                that weight be altered. As such, by default, this
                is None. If weight is to be changed, it should be a
                float.
            :param new_edge_properties: alter_edge does not require
                that edge_properties be altered. As such, by default,
                this is None. If any edge properties are to be changed,
                it should be a dictionary of edge properties to be changed.
            :return:
            """

            existing_edge = self.graph.get_edge_data(from_index, to_index)

            # ensure that edge exists before attempting to change it
            if not existing_edge:
                raise ValueError("Edge between {} and {} cannot be altered;\
                                    no edge exists between those sites.".format(
                    from_index, to_index
                ))

            # Third index should always be 0 because there should only be one edge between any two nodes
            if new_weight is not None:
                self.graph[from_index][to_index][0]['weight'] = new_weight

            if new_edge_properties is not None:
                for prop in list(new_edge_properties.keys()):
                    self.graph[from_index][to_index][0][prop] = new_edge_properties[prop]

        def break_edge(self, from_index, to_index, allow_reverse=False):
            """
            Remove an edge from the MoleculeGraph

            :param from_index: int
            :param to_index: int
            :param allow_reverse: If allow_reverse is True, then break_edge will
                attempt to break both (from_index, to_index) and, failing that,
                will attempt to break (to_index, from_index).
            :return:
            """

            # ensure that edge exists before attempting to remove it
            existing_edge = self.graph.get_edge_data(from_index, to_index)
            existing_reverse = None

            if existing_edge:
                self.graph.remove_edge(from_index, to_index)

            else:
                if allow_reverse:
                    existing_reverse = self.graph.get_edge_data(to_index,
                                                                from_index)

                if existing_reverse:
                    self.graph.remove_edge(to_index, from_index)
                else:
                    raise ValueError("Edge cannot be broken between {} and {};\
                                    no edge exists between those sites.".format(
                        from_index, to_index
                    ))

        def remove_nodes(self, indices):
            """
            A wrapper for Molecule.remove_sites().

            :param indices: list of indices in the current Molecule (and graph) to
                be removed.
            :return:
            """

            self.molecule.remove_sites(indices)
            self.graph.remove_nodes_from(indices)

            mapping = {}
            for correct, current in enumerate(sorted(self.graph.nodes)):
                mapping[current] = correct

            nx.relabel_nodes(self.graph, mapping, copy=False)
            self.set_node_attributes()

        def split_molecule_subgraphs(self, bonds, allow_reverse=False,
                                     alterations=None):
            """
            Split MoleculeGraph into two or more MoleculeGraphs by
            breaking a set of bonds. This function uses
            MoleculeGraph.break_edge repeatedly to create
            disjoint graphs (two or more separate molecules).
            This function does not only alter the graph
            information, but also changes the underlying
            Moledules.
            If the bonds parameter does not include sufficient
            bonds to separate two molecule fragments, then this
            function will fail.
            Currently, this function naively assigns the charge
            of the total molecule to a single submolecule. A
            later effort will be to actually accurately assign
            charge.
            NOTE: This function does not modify the original
            MoleculeGraph. It creates a copy, modifies that, and
            returns two or more new MoleculeGraph objects.

            :param bonds: list of tuples (from_index, to_index)
                representing bonds to be broken to split the MoleculeGraph.
            :param alterations: a dict {(from_index, to_index): alt},
                where alt is a dictionary including weight and/or edge
                properties to be changed following the split.
            :param allow_reverse: If allow_reverse is True, then break_edge will
                attempt to break both (from_index, to_index) and, failing that,
                will attempt to break (to_index, from_index).
            :return: list of MoleculeGraphs
            """

            self.set_node_attributes()

            original = copy.deepcopy(self)

            for bond in bonds:
                original.break_edge(bond[0], bond[1], allow_reverse=allow_reverse)

            if nx.is_weakly_connected(original.graph):
                raise MolGraphSplitError("Cannot split molecule; \
                                    MoleculeGraph is still connected.")
            else:

                # alter any bonds before partition, to avoid remapping
                if alterations is not None:
                    for (u, v) in alterations.keys():
                        if "weight" in alterations[(u, v)]:
                            weight = alterations[(u, v)]["weight"]
                            del alterations[(u, v)]["weight"]
                            edge_properties = alterations[(u, v)] \
                                if len(alterations[(u, v)]) != 0 else None
                            original.alter_edge(u, v, new_weight=weight,
                                                new_edge_properties=edge_properties)
                        else:
                            original.alter_edge(u, v,
                                                new_edge_properties=alterations[(u, v)])

                sub_mols = []

                # Had to use nx.weakly_connected_components because of deprecation
                # of nx.weakly_connected_component_subgraphs
                subgraphs = [original.graph.subgraph(c)
                             for c in nx.weakly_connected_components(original.graph)]

                for subg in subgraphs:

                    nodes = sorted(list(subg.nodes))

                    # Molecule indices are essentially list-based, so node indices
                    # must be remapped, incrementing from 0
                    mapping = {}
                    for i in range(len(nodes)):
                        mapping[nodes[i]] = i

                    # just give charge to whatever subgraph has node with index 0
                    # TODO: actually figure out how to distribute charge
                    if 0 in nodes:
                        charge = self.molecule.charge
                    else:
                        charge = 0

                    # relabel nodes in graph to match mapping
                    new_graph = nx.relabel_nodes(subg, mapping)

                    species = nx.get_node_attributes(new_graph, "specie")
                    coords = nx.get_node_attributes(new_graph, "coords")
                    raw_props = nx.get_node_attributes(new_graph, "properties")

                    properties = {}
                    for prop_set in raw_props.values():
                        for prop in prop_set.keys():
                            if prop in properties:
                                properties[prop].append(prop_set[prop])
                            else:
                                properties[prop] = [prop_set[prop]]

                    # Site properties must be present for all atoms in the molecule
                    # in order to be used for Molecule instantiation
                    for k, v in properties.items():
                        if len(v) != len(species):
                            del properties[k]

                    new_mol = Molecule(species, coords, charge=charge,
                                       site_properties=properties)
                    graph_data = json_graph.adjacency_data(new_graph)

                    # create new MoleculeGraph
                    sub_mols.append(MoleculeGraph(new_mol, graph_data=graph_data))

                return sub_mols

        def build_unique_fragments(self):
            """
            Find all possible fragment combinations of the MoleculeGraphs (in other
            words, all connected induced subgraphs)

            :return:
            """
            self.set_node_attributes()

            graph = self.graph.to_undirected()

            # find all possible fragments, aka connected induced subgraphs
            frag_dict = {}
            for ii in range(1, len(self.molecule)):
                for combination in combinations(graph.nodes, ii):
                    mycomp = []
                    for idx in combination:
                        mycomp.append(str(self.molecule[idx].specie))
                    mycomp = "".join(sorted(mycomp))
                    subgraph = nx.subgraph(graph, combination)
                    if nx.is_connected(subgraph):
                        mykey = mycomp + str(len(subgraph.edges()))
                        if mykey not in frag_dict:
                            frag_dict[mykey] = [copy.deepcopy(subgraph)]
                        else:
                            frag_dict[mykey].append(copy.deepcopy(subgraph))

            # narrow to all unique fragments using graph isomorphism
            unique_frag_dict = {}
            for key in frag_dict:
                unique_frags = []
                for frag in frag_dict[key]:
                    found = False
                    for f in unique_frags:
                        if _isomorphic(frag, f):
                            found = True
                            break
                    if not found:
                        unique_frags.append(frag)
                unique_frag_dict[key] = copy.deepcopy(unique_frags)

            # convert back to molecule graphs
            unique_mol_graph_dict = {}
            for key in unique_frag_dict:
                unique_mol_graph_list = []
                for fragment in unique_frag_dict[key]:
                    mapping = {e: i for i, e in enumerate(sorted(fragment.nodes))}
                    remapped = nx.relabel_nodes(fragment, mapping)

                    species = nx.get_node_attributes(remapped, "specie")
                    coords = nx.get_node_attributes(remapped, "coords")

                    edges = {}

                    for from_index, to_index, key in remapped.edges:
                        edge_props = fragment.get_edge_data(from_index, to_index, key=key)

                        edges[(from_index, to_index)] = edge_props

                    unique_mol_graph_list.append(self.with_edges(Molecule(species=species,
                                                                          coords=coords,
                                                                          charge=self.molecule.charge),
                                                                 edges))

                frag_key = str(unique_mol_graph_list[0].molecule.composition.alphabetical_formula) + " E" + str(
                    len(unique_mol_graph_list[0].graph.edges()))
                unique_mol_graph_dict[frag_key] = copy.deepcopy(unique_mol_graph_list)
            return unique_mol_graph_dict

        def substitute_group(self, index, func_grp, strategy, bond_order=1,
                             graph_dict=None, strategy_params=None):
            """
            Builds off of Molecule.substitute to replace an atom in self.molecule
            with a functional group. This method also amends self.graph to
            incorporate the new functional group.

            NOTE: using a MoleculeGraph will generally produce a different graph
            compared with using a Molecule or str (when not using graph_dict).

            :param index: Index of atom to substitute.
            :param func_grp: Substituent molecule. There are three options:

                1. Providing an actual molecule as the input. The first atom
                    must be a DummySpecie X, indicating the position of
                    nearest neighbor. The second atom must be the next
                    nearest atom. For example, for a methyl group
                    substitution, func_grp should be X-CH3, where X is the
                    first site and C is the second site. What the code will
                    do is to remove the index site, and connect the nearest
                    neighbor to the C atom in CH3. The X-C bond indicates the
                    directionality to connect the atoms.
                2. A string name. The molecule will be obtained from the
                    relevant template in func_groups.json.
                3. A MoleculeGraph object.
            :param strategy: Class from pymatgen.analysis.local_env.
            :param bond_order: A specified bond order to calculate the bond
                    length between the attached functional group and the nearest
                    neighbor site. Defaults to 1.
            :param graph_dict: Dictionary representing the bonds of the functional
                    group (format: {(u, v): props}, where props is a dictionary of
                    properties, including weight. If None, then the algorithm
                    will attempt to automatically determine bonds using one of
                    a list of strategies defined in pymatgen.analysis.local_env.
            :param strategy_params: dictionary of keyword arguments for strategy.
                    If None, default parameters will be used.
            :return:
            """

            def map_indices(grp):
                grp_map = {}

                # Get indices now occupied by functional group
                # Subtracting 1 because the dummy atom X should not count
                atoms = len(grp) - 1
                offset = len(self.molecule) - atoms

                for i in range(atoms):
                    grp_map[i] = i + offset

                return grp_map

            # Work is simplified if a graph is already in place
            if isinstance(func_grp, MoleculeGraph):

                self.molecule.substitute(index, func_grp.molecule,
                                         bond_order=bond_order)

                mapping = map_indices(func_grp.molecule)

                for (u, v) in list(func_grp.graph.edges()):
                    edge_props = func_grp.graph.get_edge_data(u, v)[0]
                    weight = None
                    if "weight" in edge_props.keys():
                        weight = edge_props["weight"]
                        del edge_props["weight"]
                    self.add_edge(mapping[u], mapping[v],
                                  weight=weight, edge_properties=edge_props)

            else:
                if isinstance(func_grp, Molecule):
                    func_grp = copy.deepcopy(func_grp)
                else:
                    try:
                        func_grp = copy.deepcopy(FunctionalGroups[func_grp])
                    except Exception:
                        raise RuntimeError("Can't find functional group in list. "
                                           "Provide explicit coordinate instead")

                self.molecule.substitute(index, func_grp, bond_order=bond_order)

                mapping = map_indices(func_grp)

                # Remove dummy atom "X"
                func_grp.remove_species("X")

                if graph_dict is not None:
                    for (u, v) in graph_dict.keys():
                        edge_props = graph_dict[(u, v)]
                        if "weight" in edge_props.keys():
                            weight = edge_props["weight"]
                            del edge_props["weight"]
                        self.add_edge(mapping[u], mapping[v],
                                      weight=weight, edge_properties=edge_props)

                else:
                    if strategy_params is None:
                        strategy_params = {}
                    strat = strategy(**strategy_params)
                    graph = self.with_local_env_strategy(func_grp, strat)

                    for (u, v) in list(graph.graph.edges()):
                        edge_props = graph.graph.get_edge_data(u, v)[0]
                        weight = None
                        if "weight" in edge_props.keys():
                            weight = edge_props["weight"]
                            del edge_props["weight"]

                        if 0 not in list(graph.graph.nodes()):
                            # If graph indices have different indexing
                            u, v = (u - 1), (v - 1)

                        self.add_edge(mapping[u], mapping[v],
                                      weight=weight, edge_properties=edge_props)

        def replace_group(self, index, func_grp, strategy, bond_order=1,
                          graph_dict=None, strategy_params=None):
            """
            Builds off of Molecule.substitute and MoleculeGraph.substitute_group
            to replace a functional group in self.molecule with a functional group.
            This method also amends self.graph to incorporate the new functional
            group.

            TODO: Figure out how to replace into a ring structure.

            :param index: Index of atom to substitute.
            :param func_grp: Substituent molecule. There are three options:

                1. Providing an actual molecule as the input. The first atom
                   must be a DummySpecie X, indicating the position of
                   nearest neighbor. The second atom must be the next
                   nearest atom. For example, for a methyl group
                   substitution, func_grp should be X-CH3, where X is the
                   first site and C is the second site. What the code will
                   do is to remove the index site, and connect the nearest
                   neighbor to the C atom in CH3. The X-C bond indicates the
                   directionality to connect the atoms.
                2. A string name. The molecule will be obtained from the
                   relevant template in func_groups.json.
                3. A MoleculeGraph object.
            :param strategy: Class from pymatgen.analysis.local_env.
            :param bond_order: A specified bond order to calculate the bond
                length between the attached functional group and the nearest
                neighbor site. Defaults to 1.
            :param graph_dict: Dictionary representing the bonds of the functional
                group (format: {(u, v): props}, where props is a dictionary of
                properties, including weight. If None, then the algorithm
                will attempt to automatically determine bonds using one of
                a list of strategies defined in pymatgen.analysis.local_env.
            :param strategy_params: dictionary of keyword arguments for strategy.
                If None, default parameters will be used.
            :return:
            """

            self.set_node_attributes()
            neighbors = self.get_connected_sites(index)

            # If the atom at index is terminal
            if len(neighbors) == 1:
                self.substitute_group(index, func_grp, strategy,
                                      bond_order=bond_order, graph_dict=graph_dict,
                                      strategy_params=strategy_params)

            else:
                rings = self.find_rings(including=[index])
                if len(rings) != 0:
                    raise RuntimeError("Currently functional group replacement"
                                       "cannot occur at an atom within a ring"
                                       "structure.")

                to_remove = set()
                sizes = dict()
                disconnected = self.graph.to_undirected()
                disconnected.remove_node(index)
                for neighbor in neighbors:
                    sizes[neighbor[2]] = len(nx.descendants(disconnected, neighbor[2]))

                keep = max(sizes, key=lambda x: sizes[x])
                for i in sizes.keys():
                    if i != keep:
                        to_remove.add(i)

                self.remove_nodes(list(to_remove))

                self.group = self.substitute_group(index, func_grp, strategy,
                                                   bond_order=bond_order,
                                                   graph_dict=graph_dict,
                                                   strategy_params=strategy_params)

        def find_rings(self, including=None):
            """
            Find ring structures in the MoleculeGraph.

            :param including: list of site indices. If
                including is not None, then find_rings will
                only return those rings including the specified
                sites. By default, this parameter is None, and
                all rings will be returned.
            :return: dict {index:cycle}. Each
                entry will be a ring (cycle, in graph theory terms) including the index
                found in the Molecule. If there is no cycle including an index, the
                value will be an empty list.
            """

            # Copies self.graph such that all edges (u, v) matched by edges (v, u)
            undirected = self.graph.to_undirected()
            directed = undirected.to_directed()

            cycles_nodes = []
            cycles_edges = []

            # Remove all two-edge cycles
            all_cycles = [c for c in nx.simple_cycles(directed) if len(c) > 2]

            # Using to_directed() will mean that each cycle always appears twice
            # So, we must also remove duplicates
            unique_sorted = []
            unique_cycles = []
            for cycle in all_cycles:
                if sorted(cycle) not in unique_sorted:
                    unique_sorted.append(sorted(cycle))
                    unique_cycles.append(cycle)

            if including is None:
                cycles_nodes = unique_cycles
            else:
                for i in including:
                    for cycle in unique_cycles:
                        if i in cycle and cycle not in cycles_nodes:
                            cycles_nodes.append(cycle)

            for cycle in cycles_nodes:
                edges = []
                for i, e in enumerate(cycle):
                    edges.append((cycle[i - 1], e))
                cycles_edges.append(edges)

            return cycles_edges

        def get_connected_sites(self, n):
            """
            Returns a named tuple of neighbors of site n:
            periodic_site, jimage, index, weight.
            Index is the index of the corresponding site
            in the original structure, weight can be
            None if not defined.
            :param n: index of Site in Molecule
            :param jimage: lattice vector of site
            :return: list of ConnectedSite tuples,
                sorted by closest first
            """

            connected_sites = set()

            out_edges = [(u, v, d) for u, v, d in self.graph.out_edges(n, data=True)]
            in_edges = [(u, v, d) for u, v, d in self.graph.in_edges(n, data=True)]

            for u, v, d in out_edges + in_edges:

                weight = d.get('weight', None)

                if v == n:
                    site = self.molecule[u]
                    dist = self.molecule[v].distance(self.molecule[u])

                    connected_site = ConnectedSite(site=site,
                                                   jimage=(0, 0, 0),
                                                   index=u,
                                                   weight=weight,
                                                   dist=dist)
                else:
                    site = self.molecule[v]
                    dist = self.molecule[u].distance(self.molecule[v])

                    connected_site = ConnectedSite(site=site,
                                                   jimage=(0, 0, 0),
                                                   index=v,
                                                   weight=weight,
                                                   dist=dist)

                connected_sites.add(connected_site)

            # return list sorted by closest sites first
            connected_sites = list(connected_sites)
            connected_sites.sort(key=lambda x: x.dist)

            return connected_sites

        def get_coordination_of_site(self, n):
            """
            Returns the number of neighbors of site n.
            In graph terms, simply returns degree
            of node corresponding to site n.
            :param n: index of site
            :return (int):
            """
            number_of_self_loops = sum([1 for n, v in self.graph.edges(n) if n == v])
            return self.graph.degree(n) - number_of_self_loops

        def draw_graph_to_file(self, filename="graph",
                               diff=None,
                               hide_unconnected_nodes=False,
                               hide_image_edges=True,
                               edge_colors=False,
                               node_labels=False,
                               weight_labels=False,
                               image_labels=False,
                               color_scheme="VESTA",
                               keep_dot=False,
                               algo="fdp"):
            """
            Draws graph using GraphViz.

            The networkx graph object itself can also be drawn
            with networkx's in-built graph drawing methods, but
            note that this might give misleading results for
            multigraphs (edges are super-imposed on each other).

            If visualization is difficult to interpret,
            `hide_image_edges` can help, especially in larger
            graphs.

            :param filename: filename to output, will detect filetype
                from extension (any graphviz filetype supported, such as
                pdf or png)
            :param diff (StructureGraph): an additional graph to
                compare with, will color edges red that do not exist in diff
                and edges green that are in diff graph but not in the
                reference graph
            :param hide_unconnected_nodes: if True, hide unconnected
                nodes
            :param hide_image_edges: if True, do not draw edges that
                go through periodic boundaries
            :param edge_colors (bool): if True, use node colors to
                color edges
            :param node_labels (bool): if True, label nodes with
                species and site index
            :param weight_labels (bool): if True, label edges with
                weights
            :param image_labels (bool): if True, label edges with
                their periodic images (usually only used for debugging,
                edges to periodic images always appear as dashed lines)
            :param color_scheme (str): "VESTA" or "JMOL"
            :param keep_dot (bool): keep GraphViz .dot file for later
                visualization
            :param algo: any graphviz algo, "neato" (for simple graphs)
                or "fdp" (for more crowded graphs) usually give good outputs
            :return:
            """

            if not which(algo):
                raise RuntimeError("StructureGraph graph drawing requires "
                                   "GraphViz binaries to be in the path.")

            # Developer note: NetworkX also has methods for drawing
            # graphs using matplotlib, these also work here. However,
            # a dedicated tool like GraphViz allows for much easier
            # control over graph appearance and also correctly displays
            # mutli-graphs (matplotlib can superimpose multiple edges).

            g = self.graph.copy()

            g.graph = {'nodesep': 10.0, 'dpi': 300, 'overlap': "false"}

            # add display options for nodes
            for n in g.nodes():
                # get label by species name
                label = "{}({})".format(str(self.molecule[n].specie), n) if node_labels else ""

                # use standard color scheme for nodes
                c = EL_COLORS[color_scheme].get(str(self.molecule[n].specie.symbol), [0, 0, 0])

                # get contrasting font color
                # magic numbers account for perceived luminescence
                # https://stackoverflow.com/questions/1855884/determine-font-color-based-on-background-color
                fontcolor = '#000000' if 1 - (c[0] * 0.299 + c[1] * 0.587
                                              + c[2] * 0.114) / 255 < 0.5 else '#ffffff'

                # convert color to hex string
                color = "#{:02x}{:02x}{:02x}".format(c[0], c[1], c[2])

                g.add_node(n, fillcolor=color, fontcolor=fontcolor, label=label,
                           fontname="Helvetica-bold", style="filled", shape="circle")

            edges_to_delete = []

            # add display options for edges
            for u, v, k, d in g.edges(keys=True, data=True):

                # retrieve from/to images, set as origin if not defined
                if "to_image" in d:
                    to_image = d['to_jimage']
                else:
                    to_image = (0, 0, 0)

                # set edge style
                d['style'] = "solid"
                if to_image != (0, 0, 0):
                    d['style'] = "dashed"
                    if hide_image_edges:
                        edges_to_delete.append((u, v, k))

                # don't show edge directions
                d['arrowhead'] = "none"

                # only add labels for images that are not the origin
                if image_labels:
                    d['headlabel'] = "" if to_image == (0, 0, 0) else "to {}".format((to_image))
                    d['arrowhead'] = "normal" if d['headlabel'] else "none"

                # optionally color edges using node colors
                color_u = g.node[u]['fillcolor']
                color_v = g.node[v]['fillcolor']
                d['color_uv'] = "{};0.5:{};0.5".format(color_u, color_v) if edge_colors else "#000000"

                # optionally add weights to graph
                if weight_labels:
                    units = g.graph.get('edge_weight_units', "")
                    if d.get('weight'):
                        d['label'] = "{:.2f} {}".format(d['weight'], units)

                # update edge with our new style attributes
                g.edges[u, v, k].update(d)

            # optionally remove periodic image edges,
            # these can be confusing due to periodic boundaries
            if hide_image_edges:
                for edge_to_delete in edges_to_delete:
                    g.remove_edge(*edge_to_delete)

            # optionally hide unconnected nodes,
            # these can appear when removing periodic edges
            if hide_unconnected_nodes:
                g = g.subgraph([n for n in g.degree() if g.degree()[n] != 0])

            # optionally highlight differences with another graph
            if diff:
                diff = self.diff(diff, strict=True)
                green_edges = []
                red_edges = []
                for u, v, k, d in g.edges(keys=True, data=True):
                    if (u, v, d['to_jimage']) in diff['self']:
                        # edge has been deleted
                        red_edges.append((u, v, k))
                    elif (u, v, d['to_jimage']) in diff['other']:
                        # edge has been added
                        green_edges.append((u, v, k))
                for u, v, k in green_edges:
                    g.edges[u, v, k].update({'color_uv': '#00ff00'})
                for u, v, k in red_edges:
                    g.edges[u, v, k].update({'color_uv': '#ff0000'})

            basename, extension = os.path.splitext(filename)
            extension = extension[1:]

            write_dot(g, basename + ".dot")

            with open(filename, "w") as f:

                args = [algo, "-T", extension, basename + ".dot"]
                rs = subprocess.Popen(args,
                                      stdout=f,
                                      stdin=subprocess.PIPE, close_fds=True)
                rs.communicate()
                if rs.returncode != 0:
                    raise RuntimeError("{} exited with return code {}.".format(algo, rs.returncode))

            if not keep_dot:
                os.remove(basename + ".dot")

        def as_dict(self):
            """
            As in :Class: `pymatgen.core.Molecule` except
            with using `to_dict_of_dicts` from NetworkX
            to store graph information.
            """

            d = {"@module": self.__class__.__module__,
                 "@class": self.__class__.__name__,
                 "molecule": self.molecule.as_dict(),
                 "graphs": json_graph.adjacency_data(self.graph)}

            return d

        @classmethod
        def from_dict(cls, d):
            """
            As in :Class: `pymatgen.core.Molecule` except
            restoring graphs using `from_dict_of_dicts`
            from NetworkX to restore graph information.
            """
            m = Molecule.from_dict(d['molecule'])
            return cls(m, d['graphs'])

        def _edges_to_string(self, g):

            header = "from    to  to_image    "
            header_line = "----  ----  ------------"
            edge_weight_name = g.graph["edge_weight_name"]
            if edge_weight_name:
                print_weights = ["weight"]
                edge_label = g.graph["edge_weight_name"]
                edge_weight_units = g.graph["edge_weight_units"]
                if edge_weight_units:
                    edge_label += " ({})".format(edge_weight_units)
                header += "  {}".format(edge_label)
                header_line += "  {}".format("-" * max([18, len(edge_label)]))
            else:
                print_weights = False

            s = header + "\n" + header_line + "\n"

            edges = list(g.edges(data=True))

            # sort edges for consistent ordering
            edges.sort(key=itemgetter(0, 1))

            if print_weights:
                for u, v, data in edges:
                    s += "{:4}  {:4}  {:12}  {:.3e}\n".format(u, v, str(data.get("to_jimage", (0, 0, 0))),
                                                              data.get("weight", 0))
            else:
                for u, v, data in edges:
                    s += "{:4}  {:4}  {:12}\n".format(u, v,
                                                      str(data.get("to_jimage", (0, 0, 0))))

            return s

        def __str__(self):
            s = "Molecule Graph"
            s += "\nMolecule: \n{}".format(self.molecule.__str__())
            s += "\nGraph: {}\n".format(self.name)
            s += self._edges_to_string(self.graph)
            return s

        def __repr__(self):
            s = "Molecule Graph"
            s += "\nMolecule: \n{}".format(self.molecule.__repr__())
            s += "\nGraph: {}\n".format(self.name)
            s += self._edges_to_string(self.graph)
            return s

        def __len__(self):
            """
            :return: length of Molecule / number of nodes in graph
            """
            return len(self.molecule)

        def sort(self, key=None, reverse=False):
            """
            Same as Molecule.sort(), also remaps nodes in graph.
            :param key:
            :param reverse:
            :return:
            """

            old_molecule = self.molecule.copy()

            # sort Molecule
            self.molecule._sites = sorted(self.molecule._sites, key=key, reverse=reverse)

            # apply Molecule ordering to graph
            mapping = {idx: self.molecule.index(site) for idx, site in enumerate(old_molecule)}
            self.graph = nx.relabel_nodes(self.graph, mapping, copy=True)

            # normalize directions of edges
            edges_to_remove = []
            edges_to_add = []
            for u, v, k, d in self.graph.edges(keys=True, data=True):
                if v < u:
                    new_v, new_u, new_d = u, v, d.copy()
                    new_d['to_jimage'] = (0, 0, 0)
                    edges_to_remove.append((u, v, k))
                    edges_to_add.append((new_u, new_v, new_d))

            # add/delete marked edges
            for edges_to_remove in edges_to_remove:
                self.graph.remove_edge(*edges_to_remove)
            for (u, v, d) in edges_to_add:
                self.graph.add_edge(u, v, **d)

        def __copy__(self):
            return MoleculeGraph.from_dict(self.as_dict())

        def __eq__(self, other):
            """
            Two MoleculeGraphs are equal if they have equal Molecules,
            and have the same edges between Sites. Edge weights can be
            different and MoleculeGraphs can still be considered equal.

            :param other: MoleculeGraph
            :return (bool):
            """

            # sort for consistent node indices
            # PeriodicSite should have a proper __hash__() value,
            # using its frac_coords as a convenient key
            try:
                mapping = {tuple(site.coords): self.molecule.index(site) for site in other.molecule}
            except ValueError:
                return False
            other_sorted = other.__copy__()
            other_sorted.sort(key=lambda site: mapping[tuple(site.coords)])

            edges = {(u, v)
                     for u, v, d in self.graph.edges(keys=False, data=True)}

            edges_other = {(u, v) for u, v, d in other_sorted.graph.edges(keys=False, data=True)}

            return (edges == edges_other) and \
                   (self.molecule == other_sorted.molecule)

        def isomorphic_to(self, other):
            """
            Checks if the graphs of two MoleculeGraphs are isomorphic to one
            another. In order to prevent problems with misdirected edges, both
            graphs are converted into undirected nx.Graph objects.

            :param other: MoleculeGraph object to be compared.
            :return: bool
            """
            if len(self.molecule) != len(other.molecule):
                return False
            elif self.molecule.composition.alphabetical_formula != other.molecule.composition.alphabetical_formula:
                return False
            elif len(self.graph.edges()) != len(other.graph.edges()):
                return False
            else:
                return _isomorphic(self.graph, other.graph)

        def diff(self, other, strict=True):
            """
            Compares two MoleculeGraphs. Returns dict with
            keys 'self', 'other', 'both' with edges that are
            present in only one MoleculeGraph ('self' and
            'other'), and edges that are present in both.

            The Jaccard distance is a simple measure of the
            dissimilarity between two MoleculeGraphs (ignoring
            edge weights), and is defined by 1 - (size of the
            intersection / size of the union) of the sets of
            edges. This is returned with key 'dist'.

            Important note: all node indices are in terms
            of the MoleculeGraph this method is called
            from, not the 'other' MoleculeGraph: there
            is no guarantee the node indices will be the
            same if the underlying Molecules are ordered
            differently.

            :param other: MoleculeGraph
            :param strict: if False, will compare bonds
                from different Molecules, with node indices
                replaced by Specie strings, will not count
                number of occurrences of bonds
            :return:
            """

            if self.molecule != other.molecule and strict:
                return ValueError("Meaningless to compare MoleculeGraphs if "
                                  "corresponding Molecules are different.")

            if strict:
                # sort for consistent node indices
                # PeriodicSite should have a proper __hash__() value,
                # using its frac_coords as a convenient key
                mapping = {tuple(site.frac_coords): self.molecule.index(site) for site in other.molecule}
                other_sorted = other.__copy__()
                other_sorted.sort(key=lambda site: mapping[tuple(site.frac_coords)])

                edges = {(u, v, d.get('to_jimage', (0, 0, 0)))
                         for u, v, d in self.graph.edges(keys=False, data=True)}

                edges_other = {(u, v, d.get('to_jimage', (0, 0, 0)))
                               for u, v, d in other_sorted.graph.edges(keys=False, data=True)}

            else:

                edges = {(str(self.molecule[u].specie),
                          str(self.molecule[v].specie))
                         for u, v, d in self.graph.edges(keys=False, data=True)}

                edges_other = {(str(other.structure[u].specie),
                                str(other.structure[v].specie))
                               for u, v, d in other.graph.edges(keys=False, data=True)}

            if len(edges) == 0 and len(edges_other) == 0:
                jaccard_dist = 0  # by definition
            else:
                jaccard_dist = 1 - len(edges.intersection(edges_other)) / len(edges.union(edges_other))

            return {
                'self': edges - edges_other,
                'other': edges_other - edges,
                'both': edges.intersection(edges_other),
                'dist': jaccard_dist
            }