pymatgen.analysis.chemenv.connectivity.connected_components — pymatgen 2020.7.3 documentation

# Source code for pymatgen.analysis.chemenv.connectivity.connected_components

    """
    Connected components.
    """

    import logging
    import itertools

    import numpy as np
    from matplotlib.patches import FancyArrowPatch, Circle

    import networkx as nx
    from networkx.algorithms.traversal import bfs_tree
    from networkx.algorithms.components import is_connected

    from monty.json import MSONable
    from monty.json import jsanitize

    from pymatgen.analysis.chemenv.utils.graph_utils import get_delta
    from pymatgen.analysis.chemenv.utils.chemenv_errors import ChemenvError
    from pymatgen.analysis.chemenv.utils.math_utils import get_linearly_independent_vectors
    from pymatgen.analysis.chemenv.connectivity.environment_nodes import EnvironmentNode

    def draw_network(env_graph, pos, ax, sg=None, periodicity_vectors=None):
        """

        Args:
            env_graph ():
            pos ():
            ax ():
            sg ():
            periodicity_vectors ():

        Returns:

        """
        for n in env_graph:
            c = Circle(pos[n], radius=0.02, alpha=0.5)
            ax.add_patch(c)
            env_graph.node[n]['patch'] = c
            x, y = pos[n]
            ax.annotate(str(n), pos[n], ha='center', va='center', xycoords='data')
        seen = {}
        e = None
        for (u, v, d) in env_graph.edges(data=True):
            n1 = env_graph.node[u]['patch']
            n2 = env_graph.node[v]['patch']
            rad = 0.1
            if (u, v) in seen:
                rad = seen.get((u, v))
                rad = (rad + np.sign(rad) * 0.1) * -1
            alpha = 0.5
            color = 'k'
            periodic_color = 'r'

            delta = get_delta(u, v, d)

            # center = get_center_of_arc(n1.center, n2.center, rad)
            n1center = np.array(n1.center)
            n2center = np.array(n2.center)
            midpoint = (n1center + n2center) / 2
            dist = np.sqrt(np.power(n2.center[0] - n1.center[0], 2) + np.power(n2.center[1] - n1.center[1], 2))
            n1c_to_n2c = n2center - n1center
            vv = np.cross(np.array([n1c_to_n2c[0], n1c_to_n2c[1], 0], np.float), np.array([0, 0, 1], np.float))
            vv /= np.linalg.norm(vv)
            midarc = midpoint + rad * dist * np.array([vv[0], vv[1]], np.float)
            xytext_offset = 0.1 * dist * np.array([vv[0], vv[1]], np.float)

            if periodicity_vectors is not None and len(periodicity_vectors) == 1:
                if np.all(np.array(delta) ==
                          np.array(periodicity_vectors[0])) or np.all(np.array(delta) ==
                                                                      -np.array(periodicity_vectors[0])):
                    e = FancyArrowPatch(n1center, n2center, patchA=n1, patchB=n2,
                                        arrowstyle='-|>',
                                        connectionstyle='arc3,rad=%s' % rad,
                                        mutation_scale=15.0,
                                        lw=2,
                                        alpha=alpha,
                                        color='r',
                                        linestyle='dashed')
                else:
                    e = FancyArrowPatch(n1center, n2center, patchA=n1, patchB=n2,
                                        arrowstyle='-|>',
                                        connectionstyle='arc3,rad=%s' % rad,
                                        mutation_scale=10.0,
                                        lw=2,
                                        alpha=alpha,
                                        color=color)
            else:
                ecolor = color if np.allclose(np.array(delta), np.zeros(3)) else periodic_color
                e = FancyArrowPatch(n1center, n2center, patchA=n1, patchB=n2,
                                    arrowstyle='-|>',
                                    connectionstyle='arc3,rad=%s' % rad,
                                    mutation_scale=10.0,
                                    lw=2,
                                    alpha=alpha,
                                    color=ecolor)
            ax.annotate(delta, midarc, ha='center', va='center', xycoords='data', xytext=xytext_offset,
                        textcoords='offset points')
            seen[(u, v)] = rad
            ax.add_patch(e)

        return e

    def make_supergraph(graph, multiplicity, periodicity_vectors):
        """

        Args:
            graph ():
            multiplicity ():
            periodicity_vectors ():

        Returns:

        """
        supergraph = nx.MultiGraph()
        print('peridoicity vectors :')
        print(periodicity_vectors)
        if isinstance(multiplicity, int) or len(multiplicity) == 1:
            mult = multiplicity if isinstance(multiplicity, int) else multiplicity[0]
            nodes = graph.nodes(data=True)
            inodes = [isite for isite, data in nodes]
            indices_nodes = {isite: inodes.index(isite) for isite in inodes}
            edges = graph.edges(data=True, keys=True)
            connecting_edges = []
            other_edges = []
            for (n1, n2, key, data) in edges:
                print(n1, n2, key, data)
                if np.all(np.array(data['delta']) == np.array(periodicity_vectors[0])):
                    connecting_edges.append((n1, n2, key, data))
                elif np.all(np.array(data['delta']) == -np.array(periodicity_vectors[0])):
                    new_data = dict(data)
                    new_data['delta'] = tuple(-np.array(data['delta']))
                    new_data['start'] = data['end']
                    new_data['end'] = data['start']
                    connecting_edges.append((n1, n2, key, new_data))
                else:
                    if not np.all(np.array(data['delta']) == 0):
                        print('delta not equal to periodicity nor 0 ... : ', n1, n2, key, data['delta'], data)
                        input('Are we ok with this ?')
                    other_edges.append((n1, n2, key, data))

            for imult in range(mult - 1):
                for n1, n2, key, data in other_edges:
                    new_data = dict(data)
                    new_data['start'] = (imult * len(nodes)) + indices_nodes[n1]
                    new_data['end'] = (imult * len(nodes)) + indices_nodes[n2]
                    supergraph.add_edge(new_data['start'], new_data['end'],
                                        key=key, attr_dict=new_data)
                for n1, n2, key, data in connecting_edges:
                    new_data = dict(data)
                    new_data['start'] = (imult * len(nodes)) + indices_nodes[n1]
                    new_data['end'] = np.mod(((imult + 1) * len(nodes)) + indices_nodes[n2], len(nodes) * mult)
                    new_data['delta'] = (0, 0, 0)
                    supergraph.add_edge(new_data['start'], new_data['end'],
                                        key=key, attr_dict=new_data)
            imult = mult - 1
            for n1, n2, key, data in other_edges:
                new_data = dict(data)
                new_data['start'] = (imult * len(nodes)) + indices_nodes[n1]
                new_data['end'] = (imult * len(nodes)) + indices_nodes[n2]
                supergraph.add_edge(new_data['start'], new_data['end'],
                                    key=key, attr_dict=new_data)
            for n1, n2, key, data in connecting_edges:
                new_data = dict(data)
                new_data['start'] = (imult * len(nodes)) + indices_nodes[n1]
                new_data['end'] = indices_nodes[n2]
                supergraph.add_edge(new_data['start'], new_data['end'],
                                    key=key, attr_dict=new_data)
            return supergraph
        else:
            raise NotImplementedError('make_supergraph not yet implemented for 2- and 3-periodic graphs')

    class ConnectedComponent(MSONable):
        """
        Class used to describe the connected components in a structure in terms of coordination environments.
        """

        def __init__(self, environments=None, links=None, environments_data=None, links_data=None, graph=None):
            """
            Constructor for the ConnectedComponent object.

            Args:
                environments: Environments in the connected component.
                links: Links between environments in the connected component.
                environments_data: Data of environment nodes.
                links_data: Data of links between environment nodes.
                graph: Graph of the connected component.

            Returns:
                ConnectedComponent: Instance of this class
            """
            self._periodicity_vectors = None
            self._primitive_reduced_connected_subgraph = None
            self._projected = False
            if graph is None:
                self._connected_subgraph = nx.MultiGraph()
                if environments_data is None:
                    self._connected_subgraph.add_nodes_from(environments)
                else:
                    for env in environments:
                        if env in environments_data:
                            self._connected_subgraph.add_node(env, **environments_data[env])
                        else:
                            self._connected_subgraph.add_node(env)
                for edge in links:
                    env_node1 = edge[0]
                    env_node2 = edge[1]
                    if len(edge) == 2:
                        key = None
                    else:
                        key = edge[2]
                    if ((not self._connected_subgraph.has_node(env_node1)) or
                            (not self._connected_subgraph.has_node(env_node2))):
                        raise ChemenvError(self.__class__, '__init__', 'Trying to add edge with some unexisting node ...')
                    if links_data is not None:
                        if (env_node1, env_node2, key) in links_data:
                            edge_data = links_data[(env_node1, env_node2, key)]
                        elif (env_node2, env_node1, key) in links_data:
                            edge_data = links_data[(env_node2, env_node1, key)]
                        elif (env_node1, env_node2) in links_data:
                            edge_data = links_data[(env_node1, env_node2)]
                        elif (env_node2, env_node1) in links_data:
                            edge_data = links_data[(env_node2, env_node1)]
                        else:
                            edge_data = None
                    else:
                        edge_data = None
                    if edge_data:
                        self._connected_subgraph.add_edge(env_node1, env_node2, key, **edge_data)
                    else:
                        self._connected_subgraph.add_edge(env_node1, env_node2, key)
            else:
                # TODO: should check a few requirements here ?
                self._connected_subgraph = graph

        def coordination_sequence(self, source_node, path_size=5, coordination='number', include_source=False):
            """Get the coordination sequence for a given node.

            Args:
                source_node: Node for which the coordination sequence is computed.
                path_size: Maximum length of the path for the coordination sequence.
                coordination: Type of coordination sequence. The default ("number") corresponds to the number
                    of environment nodes that are reachable by following paths of sizes between 1 and path_size.
                    For coordination "env:number", this resulting coordination sequence is a sequence of dictionaries
                    mapping the type of environment to the number of such environment reachable by following paths of
                    sizes between 1 and path_size.
                include_source: Whether to include the source_node in the coordination sequence.

            Returns:
                dict: Mapping between the nth "layer" of the connected component with the corresponding coordination.

            Examples:
                The corner-sharing octahedral framework (as in perovskites) have the following coordination sequence (up to
                a path of size 6) :
                {1: 6, 2: 18, 3: 38, 4: 66, 5: 102, 6: 146}
                Considering both the octahedrons and the cuboctahedrons of the typical BaTiO3 perovskite, the "env:number"
                coordination sequence (up to a path of size 6) starting on the Ti octahedron and Ba cuboctahedron
                are the following :
                Starting on the Ti octahedron : {1: {'O:6': 6, 'C:12': 8}, 2: {'O:6': 26, 'C:12': 48},
                                                 3: {'O:6': 90, 'C:12': 128}, 4: {'O:6': 194, 'C:12': 248},
                                                 5: {'O:6': 338, 'C:12': 408}, 6: {'O:6': 522, 'C:12': 608}}
                Starting on the Ba cuboctahedron : {1: {'O:6': 8, 'C:12': 18}, 2: {'O:6': 48, 'C:12': 74},
                                                    3: {'O:6': 128, 'C:12': 170}, 4: {'O:6': 248, 'C:12': 306},
                                                    5: {'O:6': 408, 'C:12': 482}, 6: {'O:6': 608, 'C:12': 698}}
                If include_source is set to True, the source node is included in the sequence, e.g. for the corner-sharing
                octahedral framework : {0: 1, 1: 6, 2: 18, 3: 38, 4: 66, 5: 102, 6: 146}. For the "env:number" coordination
                starting on a Ba cuboctahedron (as shown above), the coordination sequence is then :
                {0: {'C:12': 1}, 1: {'O:6': 8, 'C:12': 18}, 2: {'O:6': 48, 'C:12': 74}, 3: {'O:6': 128, 'C:12': 170},
                 4: {'O:6': 248, 'C:12': 306}, 5: {'O:6': 408, 'C:12': 482}, 6: {'O:6': 608, 'C:12': 698}}
            """
            if source_node not in self._connected_subgraph:
                raise ValueError('Node not in Connected Component. Cannot find coordination sequence.')
            # Example of an infinite periodic net in two dimensions consisting of a stacking of
            # A and B lines :
            #
            #     *     *     *     *     *
            #     *     *     *     *     *
            # * * A * * B * * A * * B * * A * *
            #     *     *     *     *     *
            #     *     *     *     *     *
            # * * A * * B * * A * * B * * A * *
            #     *     *     *     *     *
            #     *     *     *     *     *
            # * * A * * B * * A * * B * * A * *
            #     *     *     *     *     *
            #     *     *     *     *     *
            # * * A * * B * * A * * B * * A * *
            #     *     *     *     *     *
            #     *     *     *     *     *
            # * * A * * B * * A * * B * * A * *
            #     *     *     *     *     *
            #     *     *     *     *     *
            #
            # One possible quotient graph of this periodic net :
            #          __           __
            # (0,1,0) /  \         /  \ (0,1,0)
            #         `<--A--->---B--<´
            #            / (0,0,0) \
            #            \         /
            #             `--->---´
            #              (1,0,0)
            #
            # The "number" coordination sequence starting from any environment is : 4-8-12-16-...
            # The "env:number" coordination sequence starting from any environment is :
            # {A:2, B:2}-{A:4, B:4}-{A:6, B:6}-...
            current_delta = (0, 0, 0)
            current_ends = [(source_node, current_delta)]
            visited = {(source_node.isite, *current_delta)}
            path_len = 0
            cseq = {}
            if include_source:
                if coordination == 'number':
                    cseq[0] = 1
                elif coordination == 'env:number':
                    cseq[0] = {source_node.coordination_environment: 1}
                else:
                    raise ValueError('Coordination type "{}" is not valid for coordination_sequence.'.format(coordination))
            while path_len < path_size:
                new_ends = []
                for current_node_end, current_delta_end in current_ends:
                    for nb in self._connected_subgraph.neighbors(current_node_end):
                        for iedge, edata in self._connected_subgraph[current_node_end][nb].items():
                            new_delta = current_delta_end + get_delta(current_node_end, nb, edata)
                            if (nb.isite, *new_delta) not in visited:
                                new_ends.append((nb, new_delta))
                                visited.add((nb.isite, *new_delta))
                            if nb.isite == current_node_end.isite:  # Handle self loops
                                new_delta = current_delta_end - get_delta(current_node_end, nb, edata)
                                if (nb.isite, *new_delta) not in visited:
                                    new_ends.append((nb, new_delta))
                                    visited.add((nb.isite, *new_delta))
                current_ends = new_ends
                path_len += 1
                if coordination == 'number':
                    cseq[path_len] = len(current_ends)
                elif coordination == 'env:number':
                    myenvs = [myend.coordination_environment for myend, _ in current_ends]
                    cseq[path_len] = {myenv: myenvs.count(myenv) for myenv in set(myenvs)}
                else:
                    raise ValueError('Coordination type "{}" is not valid for coordination_sequence.'.format(coordination))
            return cseq

        def __len__(self):
            return len(self.graph)

        def compute_periodicity(self, algorithm='all_simple_paths'):
            """

            Args:
                algorithm ():

            Returns:

            """
            if algorithm == 'all_simple_paths':
                self.compute_periodicity_all_simple_paths_algorithm()
            elif algorithm == 'cycle_basis':
                self.compute_periodicity_cycle_basis()
            else:
                raise ValueError('Algorithm "{}" is not allowed to compute periodicity'.format(algorithm))
            self._order_periodicity_vectors()

        def compute_periodicity_all_simple_paths_algorithm(self):
            """

            Returns:

            """
            self_loop_nodes = list(nx.nodes_with_selfloops(self._connected_subgraph))
            all_nodes_independent_cell_image_vectors = []
            my_simple_graph = nx.Graph(self._connected_subgraph)
            for test_node in self._connected_subgraph.nodes():
                # TODO: do we need to go through all test nodes ?
                this_node_cell_img_vectors = []
                if test_node in self_loop_nodes:
                    for key, edge_data in self._connected_subgraph[test_node][test_node].items():
                        if edge_data['delta'] == (0, 0, 0):
                            raise ValueError('There should not be self loops with delta image = (0, 0, 0).')
                        this_node_cell_img_vectors.append(edge_data['delta'])
                for d1, d2 in itertools.combinations(this_node_cell_img_vectors, 2):
                    if d1 == d2 or d1 == tuple(-ii for ii in d2):
                        raise ValueError('There should not be self loops with the same (or opposite) delta image.')
                this_node_cell_img_vectors = get_linearly_independent_vectors(this_node_cell_img_vectors)
                # Here, we adopt a cutoff equal to the size of the graph, contrary to the default of networkX (size - 1),
                # because otherwise, the all_simple_paths algorithm fail when the source node is equal to the target node.
                paths = []
                # TODO: its probably possible to do just a dfs or bfs traversal instead of taking all simple paths!
                test_node_neighbors = my_simple_graph.neighbors(test_node)
                breaknodeloop = False
                for test_node_neighbor in test_node_neighbors:
                    # Special case for two nodes
                    if len(self._connected_subgraph[test_node][test_node_neighbor]) > 1:
                        this_path_deltas = []
                        node_node_neighbor_edges_data = list(self._connected_subgraph[test_node]
                                                             [test_node_neighbor].values())
                        for edge1_data, edge2_data in itertools.combinations(node_node_neighbor_edges_data, 2):
                            delta1 = get_delta(test_node, test_node_neighbor, edge1_data)
                            delta2 = get_delta(test_node_neighbor, test_node, edge2_data)
                            this_path_deltas.append(delta1 + delta2)
                        this_node_cell_img_vectors.extend(this_path_deltas)
                        this_node_cell_img_vectors = get_linearly_independent_vectors(this_node_cell_img_vectors)
                        if len(this_node_cell_img_vectors) == 3:
                            break
                    for path in nx.all_simple_paths(my_simple_graph, test_node, test_node_neighbor,
                                                    cutoff=len(self._connected_subgraph)):
                        path_indices = [nodepath.isite for nodepath in path]
                        if path_indices == [test_node.isite, test_node_neighbor.isite]:
                            continue
                        path_indices.append(test_node.isite)
                        path_indices = tuple(path_indices)
                        if path_indices not in paths:
                            paths.append(path_indices)
                        else:
                            continue
                        path.append(test_node)
                        # TODO: there are some paths that appears twice for cycles, and there are some paths that should
                        # probably not be considered
                        this_path_deltas = [np.zeros(3, np.int)]
                        for (node1, node2) in [(node1, path[inode1 + 1]) for inode1, node1 in enumerate(path[:-1])]:
                            this_path_deltas_new = []
                            for key, edge_data in self._connected_subgraph[node1][node2].items():
                                delta = get_delta(node1, node2, edge_data)
                                for current_delta in this_path_deltas:
                                    this_path_deltas_new.append(current_delta + delta)
                            this_path_deltas = this_path_deltas_new
                        this_node_cell_img_vectors.extend(this_path_deltas)
                        this_node_cell_img_vectors = get_linearly_independent_vectors(this_node_cell_img_vectors)
                        if len(this_node_cell_img_vectors) == 3:
                            breaknodeloop = True
                            break
                    if breaknodeloop:
                        break
                this_node_cell_img_vectors = get_linearly_independent_vectors(this_node_cell_img_vectors)
                independent_cell_img_vectors = this_node_cell_img_vectors
                all_nodes_independent_cell_image_vectors.append(independent_cell_img_vectors)
                # If we have found that the sub structure network is 3D-connected, we can stop ...
                if len(independent_cell_img_vectors) == 3:
                    break
            self._periodicity_vectors = []
            if len(all_nodes_independent_cell_image_vectors) != 0:
                for independent_cell_img_vectors in all_nodes_independent_cell_image_vectors:
                    if len(independent_cell_img_vectors) > len(self._periodicity_vectors):
                        self._periodicity_vectors = independent_cell_img_vectors
                    if len(self._periodicity_vectors) == 3:
                        break

        def compute_periodicity_cycle_basis(self):
            """

            Returns:

            """
            my_simple_graph = nx.Graph(self._connected_subgraph)
            cycles = nx.cycle_basis(my_simple_graph)
            all_deltas = []
            for cyc in cycles:
                mycyc = list(cyc)
                mycyc.append(cyc[0])
                this_cycle_deltas = [np.zeros(3, np.int)]
                for (node1, node2) in [(node1, mycyc[inode1 + 1]) for inode1, node1 in enumerate(mycyc[:-1])]:
                    this_cycle_deltas_new = []
                    for key, edge_data in self._connected_subgraph[node1][node2].items():
                        delta = get_delta(node1, node2, edge_data)
                        for current_delta in this_cycle_deltas:
                            this_cycle_deltas_new.append(current_delta + delta)
                    this_cycle_deltas = this_cycle_deltas_new
                all_deltas.extend(this_cycle_deltas)
                all_deltas = get_linearly_independent_vectors(all_deltas)
                if len(all_deltas) == 3:
                    self._periodicity_vectors = all_deltas
                    return
            # One has to consider pairs of nodes with parallel edges (these are not considered in the simple graph cycles)
            edges = my_simple_graph.edges()
            for n1, n2 in edges:
                if n1 == n2:
                    continue
                if len(self._connected_subgraph[n1][n2]) == 1:
                    continue
                elif len(self._connected_subgraph[n1][n2]) > 1:
                    for iedge1, iedge2 in itertools.combinations(self._connected_subgraph[n1][n2], 2):
                        e1data = self._connected_subgraph[n1][n2][iedge1]
                        e2data = self._connected_subgraph[n1][n2][iedge2]
                        current_delta = get_delta(n1, n2, e1data)
                        delta = get_delta(n2, n1, e2data)
                        current_delta += delta
                        all_deltas.append(current_delta)
                else:
                    raise ValueError('Should not be here ...')
                all_deltas = get_linearly_independent_vectors(all_deltas)
                if len(all_deltas) == 3:
                    self._periodicity_vectors = all_deltas
                    return
            self._periodicity_vectors = all_deltas

        def make_supergraph(self, multiplicity):
            """

            Args:
                multiplicity ():

            Returns:

            """
            supergraph = make_supergraph(self._connected_subgraph, multiplicity, self._periodicity_vectors)
            return supergraph

        def show_graph(self, graph=None, save_file=None, drawing_type='internal', pltshow=True):
            """

            Args:
                graph ():
                save_file ():
                drawing_type ():
                pltshow ():

            Returns:

            """
            import matplotlib.pyplot as plt

            if graph is None:
                shown_graph = self._connected_subgraph
            else:
                shown_graph = graph

            plt.figure()
            # pos = nx.spring_layout(shown_graph)
            if drawing_type == 'internal':
                pos = nx.shell_layout(shown_graph)
                ax = plt.gca()
                draw_network(shown_graph, pos, ax, periodicity_vectors=self._periodicity_vectors)
                ax.autoscale()
                plt.axis('equal')
                plt.axis('off')
                if save_file is not None:
                    plt.savefig(save_file)
                # nx.draw(self._connected_subgraph)
            elif drawing_type == 'draw_graphviz':
                import networkx
                networkx.nx_pydot.graphviz_layout(shown_graph)
            elif drawing_type == 'draw_random':
                import networkx
                networkx.draw_random(shown_graph)
            if pltshow:
                plt.show()

        @property
        def graph(self):
            """Return the graph of this connected component.

            Returns:
                MultiGraph: Networkx MultiGraph object with environment as nodes and links between these nodes as edges
                            with information about the image cell difference if any.
            """
            return self._connected_subgraph

        @property
        def is_periodic(self):
            """

            Returns:

            """
            return not self.is_0d

        @property
        def is_0d(self):
            """

            Returns:

            """
            if self._periodicity_vectors is None:
                self.compute_periodicity()
            return len(self._periodicity_vectors) == 0

        @property
        def is_1d(self):
            """

            Returns:

            """
            if self._periodicity_vectors is None:
                self.compute_periodicity()
            return len(self._periodicity_vectors) == 1

        @property
        def is_2d(self):
            """

            Returns:

            """
            if self._periodicity_vectors is None:
                self.compute_periodicity()
            return len(self._periodicity_vectors) == 2

        @property
        def is_3d(self):
            """

            Returns:

            """
            if self._periodicity_vectors is None:
                self.compute_periodicity()
            return len(self._periodicity_vectors) == 3

        @staticmethod
        def _order_vectors(vectors):
            """Orders vectors.

            First, each vector is made such that the first non-zero dimension is positive.
            Example: a periodicity vector [0, -1, 1] is transformed to [0, 1, -1].
            Then vectors are ordered based on their first element, then (if the first element
            is identical) based on their second element, then (if the first and second element
            are identical) based on their third element and so on ...
            Example: [[1, 1, 0], [0, 1, -1], [0, 1, 1]] is ordered as [[0, 1, -1], [0, 1, 1], [1, 1, 0]]
            """
            for ipv, pv in enumerate(vectors):
                nonzeros = np.nonzero(pv)[0]
                if (len(nonzeros) > 0) and (pv[nonzeros[0]] < 0):
                    vectors[ipv] = -pv
            return sorted(vectors, key=lambda x: x.tolist())

        def _order_periodicity_vectors(self):
            """Orders the periodicity vectors.
            """
            if len(self._periodicity_vectors) > 3:
                raise ValueError('Number of periodicity vectors is larger than 3.')
            self._periodicity_vectors = self._order_vectors(self._periodicity_vectors)
            # for ipv, pv in enumerate(self._periodicity_vectors):
            #     nonzeros = np.nonzero(pv)[0]
            #     if (len(nonzeros) > 0) and (pv[nonzeros[0]] < 0):
            #         self._periodicity_vectors[ipv] = -pv
            # self._periodicity_vectors = sorted(self._periodicity_vectors, key=lambda x: x.tolist())

        @property
        def periodicity_vectors(self):
            """

            Returns:

            """
            if self._periodicity_vectors is None:
                self.compute_periodicity()
            return [np.array(pp) for pp in self._periodicity_vectors]

        @property
        def periodicity(self):
            """

            Returns:

            """
            if self._periodicity_vectors is None:
                self.compute_periodicity()
            return '{:d}D'.format(len(self._periodicity_vectors))

        def elastic_centered_graph(self, start_node=None):
            """

            Args:
                start_node ():

            Returns:

            """
            logging.info('In elastic centering')
            # Loop on start_nodes, sometimes some nodes cannot be elastically taken
            # inside the cell if you start from a specific node
            ntest_nodes = 0
            start_node = list(self.graph.nodes())[0]

            ntest_nodes += 1
            centered_connected_subgraph = nx.MultiGraph()
            centered_connected_subgraph.add_nodes_from(self.graph.nodes())
            centered_connected_subgraph.add_edges_from(self.graph.edges(data=True))
            tree = bfs_tree(G=self.graph, source=start_node)

            current_nodes = [start_node]
            nodes_traversed = [start_node]

            inode = 0
            # Loop on "levels" in the tree
            tree_level = 0
            while True:
                tree_level += 1
                logging.debug('In tree level {:d} ({:d} nodes)'.format(tree_level, len(current_nodes)))
                new_current_nodes = []
                # Loop on nodes in this level of the tree
                for node in current_nodes:
                    inode += 1
                    logging.debug('  In node #{:d}/{:d} in level {:d} ({})'.format(inode, len(current_nodes),
                                                                                   tree_level, str(node)))
                    node_neighbors = list(tree.neighbors(n=node))
                    node_edges = centered_connected_subgraph.edges(nbunch=[node],
                                                                   data=True, keys=True)
                    # Loop on neighbors of a node (from the tree used)
                    for inode_neighbor, node_neighbor in enumerate(node_neighbors):
                        logging.debug('    Testing neighbor #{:d}/{:d} ({}) of node #{:d} ({})'.format(inode_neighbor,
                                                                                                       len(node_neighbors),
                                                                                                       node_neighbor,
                                                                                                       inode,
                                                                                                       node))
                        already_inside = False
                        ddeltas = []
                        for n1, n2, key, edata in node_edges:
                            if (n1 == node and n2 == node_neighbor) or (n2 == node and n1 == node_neighbor):
                                if edata['delta'] == (0, 0, 0):
                                    already_inside = True
                                    thisdelta = edata['delta']
                                else:
                                    if edata['start'] == node.isite and edata['end'] != node.isite:
                                        thisdelta = edata['delta']
                                    elif edata['end'] == node.isite:
                                        thisdelta = tuple([-dd for dd in edata['delta']])
                                    else:
                                        raise ValueError("Should not be here ...")
                                ddeltas.append(thisdelta)
                        logging.debug('        ddeltas : {}'.format(', '.join(['({})'.format(', '.join(str(ddd)
                                                                                                       for ddd in dd))
                                                                               for dd in ddeltas])))
                        if ddeltas.count((0, 0, 0)) > 1:
                            raise ValueError('Should not have more than one 000 delta ...')
                        if already_inside:
                            logging.debug('          Edge inside the cell ... continuing to next neighbor')
                            continue
                        logging.debug('          Edge outside the cell ... getting neighbor back inside')
                        if (0, 0, 0) in ddeltas:
                            ddeltas.remove((0, 0, 0))
                        myddelta = np.array(ddeltas[0], np.int)
                        node_neighbor_edges = centered_connected_subgraph.edges(nbunch=[node_neighbor],
                                                                                data=True, keys=True)
                        logging.debug('            Delta image from node {} to neighbor {} : '
                                      '{}'.format(str(node),
                                                  str(node_neighbor),
                                                  '({})'.format(', '.join([str(iii) for iii in myddelta]))))
                        # Loop on the edges of this neighbor
                        for n1, n2, key, edata in node_neighbor_edges:
                            if ((n1 == node_neighbor and n2 != node_neighbor) or
                                    (n2 == node_neighbor and n1 != node_neighbor)):
                                if edata['start'] == node_neighbor.isite and edata['end'] != node_neighbor.isite:
                                    centered_connected_subgraph[n1][n2][key]['delta'] = tuple([ii
                                                                                               for ii in
                                                                                               np.array(edata['delta'],
                                                                                                        np.int) + myddelta])
                                elif edata['end'] == node_neighbor.isite:
                                    centered_connected_subgraph[n1][n2][key]['delta'] = tuple([ii
                                                                                               for ii in
                                                                                               np.array(edata['delta'],
                                                                                                        np.int) - myddelta])
                                else:
                                    raise ValueError('DUHH')
                                logging.debug('                  {} to node {} now has delta '
                                              '{}'.format(str(n1), str(n2),
                                                          str(centered_connected_subgraph[n1][n2][key]['delta'])))
                    new_current_nodes.extend(node_neighbors)
                    nodes_traversed.extend(node_neighbors)
                current_nodes = new_current_nodes
                if not current_nodes:
                    break

            # Check if the graph is indeed connected if "periodic" edges (i.e. whose "delta" is not 0, 0, 0) are removed
            check_centered_connected_subgraph = nx.MultiGraph()
            check_centered_connected_subgraph.add_nodes_from(centered_connected_subgraph.nodes())
            check_centered_connected_subgraph.add_edges_from(
                [e for e in centered_connected_subgraph.edges(data=True)
                 if np.allclose(e[2]['delta'], np.zeros(3))])
            if not is_connected(check_centered_connected_subgraph):
                raise RuntimeError('Could not find a centered graph.')
            return centered_connected_subgraph

        @staticmethod
        def _edgekey_to_edgedictkey(key):
            if isinstance(key, int):
                return str(key)
            elif isinstance(key, str):
                try:
                    int(key)
                    raise RuntimeError('Cannot pass an edge key which is a str '
                                       'representation of an int.')
                except ValueError:
                    return key
            else:
                raise ValueError('Edge key should be either a str or an int.')

        @staticmethod
        def _edgedictkey_to_edgekey(key):
            if isinstance(key, int):
                return key
            elif isinstance(key, str):
                try:
                    int(key)
                except ValueError:
                    return key
            else:
                raise ValueError('Edge key in a dict of dicts representation of a graph'
                                 'should be either a str or an int.')

        @staticmethod
        def _retuplify_edgedata(edata):
            """
            Private method used to cast back lists to tuples where applicable in an edge data.

            The format of the edge data is :
            {'start': STARTINDEX, 'end': ENDINDEX, 'delta': TUPLE(DELTAX, DELTAY, DELTAZ),
             'ligands': [TUPLE(LIGAND_1_INDEX, TUPLE(DELTAX_START_LIG_1, DELTAY_START_LIG_1, DELTAZ_START_LIG_1),
                                               TUPLE(DELTAX_END_LIG_1, DELTAY_END_LIG_1, DELTAZ_END_LIG_1)),
                         TUPLE(LIGAND_2_INDEX, ...),
                         ... ]}
            When serializing to json/bson, these tuples are transformed into lists. This method transforms these lists
            back to tuples.

            Args:
                edata (dict): Edge data dictionary with possibly the above tuples as lists.

            Returns:
                dict: Edge data dictionary with the lists tranformed back into tuples when applicable.
            """
            edata['delta'] = tuple(edata['delta'])
            edata['ligands'] = [tuple([lig[0], tuple(lig[1]), tuple(lig[2])])
                                for lig in edata['ligands']]
            return edata

        def as_dict(self):
            """
            Bson-serializable dict representation of the ConnectedComponent object.

            Returns:
                dict: Bson-serializable dict representation of the ConnectedComponent object.
            """
            nodes = {'{:d}'.format(node.isite): (node, data) for node, data in self._connected_subgraph.nodes(data=True)}
            node2stringindex = {node: strindex for strindex, (node, data) in nodes.items()}
            dict_of_dicts = nx.to_dict_of_dicts(self._connected_subgraph)
            new_dict_of_dicts = {}
            for n1, n2dict in dict_of_dicts.items():
                in1 = node2stringindex[n1]
                new_dict_of_dicts[in1] = {}
                for n2, edges_dict in n2dict.items():
                    in2 = node2stringindex[n2]
                    new_dict_of_dicts[in1][in2] = {}
                    for ie, edge_data in edges_dict.items():
                        ied = self._edgekey_to_edgedictkey(ie)
                        new_dict_of_dicts[in1][in2][ied] = jsanitize(edge_data)
            return {"@module": self.__class__.__module__,
                    "@class": self.__class__.__name__,
                    "nodes": {strindex: (node.as_dict(), data) for strindex, (node, data) in nodes.items()},
                    "graph": new_dict_of_dicts}

        @classmethod
        def from_dict(cls, d):
            """
            Reconstructs the ConnectedComponent object from a dict representation of the
            ConnectedComponent object created using the as_dict method.

            Args:
                d (dict): dict representation of the ConnectedComponent object
            Returns:
                ConnectedComponent: The connected component representing the links of a given set of environments.
            """
            nodes_map = {inode_str: EnvironmentNode.from_dict(nodedict)
                         for inode_str, (nodedict, nodedata) in d['nodes'].items()}
            nodes_data = {inode_str: nodedata
                          for inode_str, (nodedict, nodedata) in d['nodes'].items()}
            dod = {}
            for e1, e1dict in d['graph'].items():
                dod[e1] = {}
                for e2, e2dict in e1dict.items():
                    dod[e1][e2] = {cls._edgedictkey_to_edgekey(ied): cls._retuplify_edgedata(edata)
                                   for ied, edata in e2dict.items()}
            graph = nx.from_dict_of_dicts(dod, create_using=nx.MultiGraph, multigraph_input=True)
            nx.set_node_attributes(graph, nodes_data)
            nx.relabel_nodes(graph, nodes_map, copy=False)
            return cls(graph=graph)

        @classmethod
        def from_graph(cls, g):
            """
            Constructor for the ConnectedComponent object from a graph of the connected component

            Args:
                g (MultiGraph): Graph of the connected component.
            Returns:
                ConnectedComponent: The connected component representing the links of a given set of environments.
            """
            return cls(graph=g)

        def description(self, full=False):
            """

            Args:
                full ():

            Returns:

            """
            out = ['Connected component with environment nodes :']
            if not full:
                out.extend([str(en) for en in sorted(self.graph.nodes())])
                return '\n'.join(out)
            for en in sorted(self.graph.nodes()):
                out.append('{}, connected to :'.format(str(en)))
                en_neighbs = nx.neighbors(self.graph, en)
                for en_neighb in sorted(en_neighbs):
                    out.append('  - {} with delta image cells'.format(en_neighb))
                    all_deltas = sorted([get_delta(node1=en, node2=en_neighb,
                                                   edge_data=edge_data).tolist()
                                         for iedge, edge_data in self.graph[en][en_neighb].items()])
                    out.extend(['     ({:d} {:d} {:d})'.format(delta[0], delta[1], delta[2]) for delta in all_deltas])
            return '\n'.join(out)