connected_components.py

"""
Connected components.
"""

from __future__ import annotations

import itertools
import logging

import networkx as nx
import numpy as np
from matplotlib.patches import Circle, FancyArrowPatch
from monty.json import MSONable, jsanitize
from networkx.algorithms.components import is_connected
from networkx.algorithms.traversal import bfs_tree

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


def draw_network(env_graph, pos, ax, sg=None, periodicity_vectors=None):
    """Draw network of environments in a matplotlib figure axes.

    Args:
        env_graph: Graph of environments.
        pos: Positions of the nodes of the environments in the 2D figure.
        ax: Axes object in which the network should be drawn.
        sg: Not used currently (drawing of supergraphs).
        periodicity_vectors: List of periodicity vectors that should be drawn.

    Returns: None

    """
    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=f"arc3,{rad=}",
                    mutation_scale=15.0,
                    lw=2,
                    alpha=alpha,
                    color="r",
                    linestyle="dashed",
                )
            else:
                e = FancyArrowPatch(
                    n1center,
                    n2center,
                    patchA=n1,
                    patchB=n2,
                    arrowstyle="-|>",
                    connectionstyle=f"arc3,{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=f"arc3,{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)


def make_supergraph(graph, multiplicity, periodicity_vectors):
    """Make supergraph from a graph of environments.

    Args:
        graph: Graph of environments.
        multiplicity: Multiplicity of the supergraph.
        periodicity_vectors: Periodicity vectors needed to make the supergraph.

    Returns: Super graph of the environments.

    """
    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

    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,
    ) -> 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: list[list] | None = 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(f"Coordination type {coordination!r} is not valid for coordination_sequence.")
        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 edata in self._connected_subgraph[current_node_end][nb].values():
                        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(f"Coordination type {coordination!r} is not valid for coordination_sequence.")
        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(f"Algorithm {algorithm!r} is not allowed to compute periodicity")
        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 edge_data in self._connected_subgraph[test_node][test_node].values():
                    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)
            break_node_loop = 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 = [node_path.isite for node_path 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, int)]
                    for node1, node2 in [(node1, path[inode1 + 1]) for inode1, node1 in enumerate(path[:-1])]:
                        this_path_deltas_new = []
                        for edge_data in self._connected_subgraph[node1][node2].values():
                            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:
                        break_node_loop = True
                        break
                if break_node_loop:
                    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, int)]
            for node1, node2 in [(node1, mycyc[inode1 + 1]) for inode1, node1 in enumerate(mycyc[:-1])]:
                this_cycle_deltas_new = []
                for edge_data in self._connected_subgraph[node1][node2].values():
                    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:
                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
            if 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) -> None:
        """
        Args:
            graph ():
            save_file ():
            drawing_type ():
            pltshow ():
        """
        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) -> bool:
        """
        Returns:
        """
        return not self.is_0d

    @property
    def is_0d(self) -> bool:
        """
        Returns:
        """
        if self._periodicity_vectors is None:
            self.compute_periodicity()
        assert self._periodicity_vectors is not None  # fix mypy arg 1 to len has incompatible type Optional
        return len(self._periodicity_vectors) == 0

    @property
    def is_1d(self) -> bool:
        """
        Returns:
        """
        if self._periodicity_vectors is None:
            self.compute_periodicity()
        assert self._periodicity_vectors is not None  # fix mypy arg 1 to len has incompatible type Optional
        return len(self._periodicity_vectors) == 1

    @property
    def is_2d(self) -> bool:
        """
        Returns:
        """
        if self._periodicity_vectors is None:
            self.compute_periodicity()
        assert self._periodicity_vectors is not None  # fix mypy arg 1 to len has incompatible type Optional
        return len(self._periodicity_vectors) == 2

    @property
    def is_3d(self) -> bool:
        """
        Returns:
        """
        if self._periodicity_vectors is None:
            self.compute_periodicity()
        assert self._periodicity_vectors is not None  # fix mypy arg 1 to len has incompatible type Optional
        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 pv[nonzeros[0]] < 0 < len(nonzeros):
                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 f"{len(self._periodicity_vectors):d}D"

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

        Returns:
            nx.MultiGraph: Elastic centered subgraph.
        """
        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(f"In tree level {tree_level:d} ({len(current_nodes):d} nodes)")
            new_current_nodes = []
            # Loop on nodes in this level of the tree
            for node in current_nodes:
                inode += 1
                logging.debug(f"  In node #{inode:d}/{len(current_nodes):d} in level {tree_level:d} ({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(
                        f"    Testing neighbor #{inode_neighbor:d}/{len(node_neighbors):d} ({node_neighbor}) of "
                        f"node #{inode:d} ({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 : " + ", ".join(f"({', '.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], int)
                    node_neighbor_edges = centered_connected_subgraph.edges(
                        nbunch=[node_neighbor], data=True, keys=True
                    )
                    logging.debug(
                        f"            Delta image from node {str(node)} to neighbor {str(node_neighbor)} : "
                        f"({', '.join(map(str, 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(
                                    np.array(edata["delta"], int) + myddelta
                                )
                            elif edata["end"] == node_neighbor.isite:
                                centered_connected_subgraph[n1][n2][key]["delta"] = tuple(
                                    np.array(edata["delta"], int) - myddelta
                                )
                            else:
                                raise ValueError("DUHH")
                            logging.debug(
                                f"                  {n1} to node {n2} now has delta "
                                f"{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)
        if 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
        raise ValueError("Edge key should be either a str or an int.")

    @staticmethod
    def _edgedictkey_to_edgekey(key):
        if isinstance(key, int):
            return key
        if isinstance(key, str):
            try:
                return 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 transformed 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 = {f"{node.isite:d}": (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": type(self).__module__,
            "@class": type(self).__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 (bool): Whether to return a short or full description.

        Returns:
            str: A description of the connected component.
        """
        out = ["Connected component with environment nodes :"]
        if not full:
            out.extend(map(str, sorted(self.graph.nodes())))
            return "\n".join(out)
        for en in sorted(self.graph.nodes()):
            out.append(f"{en}, connected to :")
            en_neighbs = nx.neighbors(self.graph, en)
            for en_neighb in sorted(en_neighbs):
                out.append(f"  - {en_neighb} with delta image cells")
                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([f"     ({delta[0]:d} {delta[1]:d} {delta[2]:d})" for delta in all_deltas])
        return "\n".join(out)