Source code for graspologic.partition.leiden

# Copyright (c) Microsoft Corporation.
# Licensed under the MIT license.

from typing import Any, Dict, List, NamedTuple, Optional, Tuple, Union
import networkx as nx
import numpy as np
import scipy
from .. import utils

import graspologic_native as gn


def _validate_and_build_edge_list(
    graph: Union[
        List[Tuple[Any, Any, Union[int, float]]],
        nx.Graph,
        np.ndarray,
        scipy.sparse.csr.csr_matrix,
    ],
    is_weighted: Optional[bool],
    weight_attribute: str,
    check_directed: bool,
    weight_default: float,
) -> List[Tuple[str, str, float]]:
    if isinstance(graph, (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph)):
        raise TypeError("directed or multigraphs are not supported in these functions")
    if (
        isinstance(graph, (np.ndarray, scipy.sparse.csr.csr_matrix))
        and check_directed is True
        and not utils.is_almost_symmetric(graph)
    ):
        raise ValueError(
            "leiden only supports undirected graphs and the adjacency matrix provided "
            "was found to be directed"
        )

    return utils.to_weighted_edge_list(
        graph=graph,
        weight_attribute=weight_attribute,
        weight_default=weight_default,
        is_weighted=is_weighted,
        is_directed=False,
    )


def _validate_common_arguments(
    starting_communities: Optional[Dict[str, int]] = None,
    extra_forced_iterations: int = 0,
    resolution: float = 1.0,
    randomness: float = 0.001,
    use_modularity: bool = True,
    random_seed: Optional[int] = None,
    is_weighted: Optional[bool] = None,
    weight_default: float = 1.0,
    check_directed: bool = True,
):
    if starting_communities is not None and not isinstance(starting_communities, dict):
        raise TypeError("starting_communities must be a dictionary")
    if not isinstance(extra_forced_iterations, int):
        raise TypeError("iterations must be an int")
    if not isinstance(resolution, (int, float)):
        raise TypeError("resolution must be a float")
    if not isinstance(randomness, (int, float)):
        raise TypeError("randomness must be a float")
    if not isinstance(use_modularity, bool):
        raise TypeError("use_modularity must be a bool")
    if random_seed is not None and not isinstance(random_seed, int):
        raise TypeError("random_seed must either be an int or None")
    if is_weighted is not None and not isinstance(is_weighted, bool):
        raise TypeError("is_weighted must either be a bool or None")
    if not isinstance(weight_default, (int, float)):
        raise TypeError("weight_default must be a float")
    if not isinstance(check_directed, bool):
        raise TypeError("check_directed must be a bool")

    if extra_forced_iterations < 0:
        raise ValueError("iterations must be a non negative integer")
    if resolution <= 0:
        raise ValueError("resolution must be a positive float")
    if randomness <= 0:
        raise ValueError("randomness must be a positive float")
    if random_seed is not None and random_seed <= 0:
        raise ValueError(
            "random_seed must be a positive integer (the native PRNG implementation is"
            " an unsigned 64 bit integer)"
        )


[docs]def leiden( graph: Union[ List[Tuple[Any, Any, Union[int, float]]], nx.Graph, np.ndarray, scipy.sparse.csr.csr_matrix, ], starting_communities: Optional[Dict[str, int]] = None, extra_forced_iterations: int = 0, resolution: float = 1.0, randomness: float = 0.001, use_modularity: bool = True, random_seed: Optional[int] = None, weight_attribute: str = "weight", is_weighted: Optional[bool] = None, weight_default: float = 1.0, check_directed: bool = True, ) -> Dict[str, int]: """ Leiden is a global network partitioning algorithm. Given a graph, it will iterate through the network node by node, and test for an improvement in our quality maximization function by speculatively joining partitions of each neighboring node. This process continues until no moves are made that increases the partitioning quality. Parameters ---------- graph : Union[List[Tuple[Any, Any, Union[int, float]]], nx.Graph, np.ndarray, scipy.sparse.csr.csr_matrix] A graph representation, whether a weighted edge list referencing an undirected graph, an undirected networkx graph, or an undirected adjacency matrix in either numpy.ndarray or scipy.sparse.csr.csr_matrix form. starting_communities : Optional[Dict[str, int]] Default is ``None``. An optional community mapping dictionary that contains the string representation of the node and the community it belongs to. Note this map must contain precisely the same nodes as the graph and every node must have a positive community id. This mapping forms the starting point of Leiden clustering and can be very useful in saving the state of a previous partition schema from a previous graph and then adjusting the graph based on new temporal data (additions, removals, weight changes, connectivity changes, etc). New nodes should get their own unique community positive integer, but the original partition can be very useful to speed up future runs of leiden. If no community map is provided, the default behavior is to create a node community identity map, where every node is in their own community. extra_forced_iterations : int Default is ``0``. Leiden will run until a maximum quality score has been found for the node clustering and no nodes are moved to a new cluster in another iteration. As there is an element of randomness to the Leiden algorithm, it is sometimes useful to set ``extra_forced_iterations`` to a number larger than 0 where the entire process is forced to attempt further refinement. resolution : float Default is ``1.0``. Higher resolution values lead to more communities and lower resolution values leads to fewer communities. Must be greater than 0. randomness : float Default is ``0.001``. The larger the randomness value, the more exploration of the partition space is possible. This is a major difference from the Louvain algorithm, which is purely greedy in the partition exploration. use_modularity : bool Default is ``True``. If ``False``, will use a Constant Potts Model (CPM). random_seed : Optional[int] Default is ``None``. Can provide an optional seed to the PRNG used in Leiden for deterministic output. weight_attribute : str Default is ``weight``. Only used when creating a weighed edge list of tuples when the source graph is a networkx graph. This attribute corresponds to the edge data dict key. is_weighted : Optional[bool] Default is ``None``. Only used when creating a weighted edge list of tuples when the source graph is an adjacency matrix. The :func:`graspologic.utils.to_weighted_edge_list` function will scan these matrices and attempt to determine whether it is weighted or not. This flag can short circuit this test and the values in the adjacency matrix will be treated as weights. weight_default : float Default is ``1.0``. If the graph is a networkx graph and the graph does not have a fully weighted sequence of edges, this default will be used. If the adjacency matrix is found or specified to be unweighted, this weight_default will be used for every edge. check_directed : bool Default is ``True``. If the graph is an adjacency matrix, we will attempt to ascertain whether it is directed or undirected. As our leiden implementation is only known to work with an undirected graph, this function will raise an error if it is found to be a directed graph. If you know it is undirected and wish to avoid this scan, you can set this value to ``False`` and only the lower triangle of the adjacency matrix will be used to generate the weighted edge list. Returns ------- Dict[str, int] The results of running leiden over the provided graph, a dictionary containing mappings of node -> community id. The keys in the dictionary are the string representations of the nodes. Raises ------ ValueError TypeError See Also -------- graspologic.utils.to_weighted_edge_list References ---------- .. [1] Traag, V.A.; Waltman, L.; Van, Eck N.J. "From Louvain to Leiden: guaranteeing well-connected communities", Scientific Reports, Vol. 9, 2019 .. [2] https://github.com/microsoft/graspologic-native Notes ----- This function is implemented in the `graspologic-native` Python module, a module written in Rust for Python. """ _validate_common_arguments( starting_communities, extra_forced_iterations, resolution, randomness, use_modularity, random_seed, is_weighted, weight_default, check_directed, ) graph = _validate_and_build_edge_list( graph, is_weighted, weight_attribute, check_directed, weight_default ) _improved, _modularity, partitions = gn.leiden( edges=graph, starting_communities=starting_communities, resolution=resolution, randomness=randomness, iterations=extra_forced_iterations + 1, use_modularity=use_modularity, seed=random_seed, ) return partitions
[docs]class HierarchicalCluster(NamedTuple): node: str cluster: int parent_cluster: Optional[int] level: int is_final_cluster: bool @classmethod def from_native( cls, native_cluster: gn.HierarchicalCluster ) -> "HierarchicalCluster": if not isinstance(native_cluster, gn.HierarchicalCluster): raise TypeError( "This class method is only valid for graspologic_native.HierarchicalCluster" ) return cls( node=native_cluster.node, cluster=native_cluster.cluster, parent_cluster=native_cluster.parent_cluster, level=native_cluster.level, is_final_cluster=native_cluster.is_final_cluster, ) @staticmethod def final_hierarchical_clustering( hierarchical_clusters: List[ Union["HierarchicalCluster", gn.HierarchicalCluster] ], ) -> Dict[str, int]: if not isinstance(hierarchical_clusters, list): raise TypeError( "This static method requires a list of hierarchical clusters" ) final_clusters = ( cluster for cluster in hierarchical_clusters if cluster.is_final_cluster ) return {cluster.node: cluster.cluster for cluster in final_clusters}
[docs]def hierarchical_leiden( graph: Union[List[Tuple[str, str, float]], nx.Graph], max_cluster_size: int = 1000, starting_communities: Optional[Dict[str, int]] = None, extra_forced_iterations: int = 0, resolution: float = 1.0, randomness: float = 0.001, use_modularity: bool = True, random_seed: Optional[int] = None, weight_attribute: str = "weight", is_weighted: Optional[bool] = None, weight_default: float = 1.0, check_directed: bool = True, ) -> List[HierarchicalCluster]: """ Leiden is a global network partitioning algorithm. Given a graph, it will iterate through the network node by node, and test for an improvement in our quality maximization function by speculatively joining partitions of each neighboring node. This process continues until no moves are made that increases the partitioning quality. Unlike the function :func:`graspologic.partition.leiden`, this function does not stop after maximization has been achieved. On some large graphs, it's useful to identify particularly large communities whose membership counts exceed ``max_cluster_size`` and induce a subnetwork solely out of that community. This subnetwork is then treated as a wholly separate entity, leiden is run over it, and the new, smaller communities are then mapped into the original community map space. The results also differ substantially; the returned List[HierarchicalCluster] is more of a log of state at each level. All HierarchicalClusters at level 0 should be considered to be the results of running :func:`graspologic.partition.leiden`. Every community whose membership is greater than ``max_cluster_size`` will then also have entries where level == 1, and so on until no communities are greater in population than ``max_cluster_size`` OR we are unable to break them down any further. Once a node's membership registration in a community cannot be changed any further, it is marked with the flag ``graspologic.partition.HierarchicalCluster.is_final_cluster = 1``. Parameters ---------- graph : Union[List[Tuple[Any, Any, Union[int, float]]], nx.Graph, np.ndarray, scipy.sparse.csr.csr_matrix] A graph representation, whether a weighted edge list referencing an undirected graph, an undirected networkx graph, or an undirected adjacency matrix in either numpy.ndarray or scipy.sparse.csr.csr_matrix form. max_cluster_size : int Default is ``1000``. Any partition or cluster with membership >= ``max_cluster_size`` will be isolated into a subnetwork. This subnetwork will be used for a new leiden global partition mapping, which will then be remapped back into the global space after completion. Once all clusters with membership >= ``max_cluster_size`` have been completed, the level increases and the partition scheme is scanned again for any new clusters with membership >= ``max_cluster_size`` and the process continues until every cluster's membership is < ``max_cluster_size`` or if they cannot be broken into more than one new community. starting_communities : Optional[Dict[str, int]] Default is ``None``. An optional community mapping dictionary that contains the string representation of the node and the community it belongs to. Note this map must contain precisely the same nodes as the graph and every node must have a positive community id. This mapping forms the starting point of Leiden clustering and can be very useful in saving the state of a previous partition schema from a previous graph and then adjusting the graph based on new temporal data (additions, removals, weight changes, connectivity changes, etc). New nodes should get their own unique community positive integer, but the original partition can be very useful to speed up future runs of leiden. If no community map is provided, the default behavior is to create a node community identity map, where every node is in their own community. extra_forced_iterations : int Default is ``0``. Leiden will run until a maximum quality score has been found for the node clustering and no nodes are moved to a new cluster in another iteration. As there is an element of randomness to the Leiden algorithm, it is sometimes useful to set ``extra_forced_iterations`` to a number larger than 0 where the entire process is forced to attempt further refinement. resolution : float Default is ``1.0``. Higher resolution values lead to more communities and lower resolution values leads to fewer communities. Must be greater than 0. randomness : float Default is ``0.001``. The larger the randomness value, the more exploration of the partition space is possible. This is a major difference from the Louvain algorithm, which is purely greedy in the partition exploration. use_modularity : bool Default is ``True``. If ``False``, will use a Constant Potts Model (CPM). random_seed : Optional[int] Default is ``None``. Can provide an optional seed to the PRNG used in Leiden for deterministic output. weight_attribute : str Default is ``weight``. Only used when creating a weighed edge list of tuples when the source graph is a networkx graph. This attribute corresponds to the edge data dict key. is_weighted : Optional[bool] Default is ``None``. Only used when creating a weighted edge list of tuples when the source graph is an adjacency matrix. The :func:`graspologic.utils.to_weighted_edge_list` function will scan these matrices and attempt to determine whether it is weighted or not. This flag can short circuit this test and the values in the adjacency matrix will be treated as weights. weight_default : float Default is ``1.0``. If the graph is a networkx graph and the graph does not have a fully weighted sequence of edges, this default will be used. If the adjacency matrix is found or specified to be unweighted, this weight_default will be used for every edge. check_directed : bool Default is ``True``. If the graph is an adjacency matrix, we will attempt to ascertain whether it is directed or undirected. As our leiden implementation is only known to work with an undirected graph, this function will raise an error if it is found to be a directed graph. If you know it is undirected and wish to avoid this scan, you can set this value to ``False`` and only the lower triangle of the adjacency matrix will be used to generate the weighted edge list. Returns ------- List[HierarchicalCluster] The results of running hierarchical leiden over the provided graph, a list of HierarchicalClusters identifying the state of every node and cluster at each level. The function :func:`graspologic.partition.HierarchicalCluster.final_hierarchical_clustering` can be used to create a dictionary mapping of node -> cluster ID Raises ------ ValueError TypeError See Also -------- graspologic.utils.to_weighted_edge_list References ---------- .. [1] Traag, V.A.; Waltman, L.; Van, Eck N.J. "From Louvain to Leiden: guaranteeing well-connected communities",Scientific Reports, Vol. 9, 2019 .. [2] https://github.com/microsoft/graspologic-native Notes ----- This function is implemented in the `graspologic-native` Python module, a module written in Rust for Python. """ _validate_common_arguments( starting_communities, extra_forced_iterations, resolution, randomness, use_modularity, random_seed, is_weighted, weight_default, check_directed, ) if not isinstance(max_cluster_size, int): raise TypeError("max_cluster_size must be an int") if max_cluster_size <= 0: raise ValueError("max_cluster_size must be a positive int") graph = _validate_and_build_edge_list( graph, is_weighted, weight_attribute, check_directed, weight_default ) hierarchical_clusters_native = gn.hierarchical_leiden( edges=graph, starting_communities=starting_communities, resolution=resolution, randomness=randomness, iterations=extra_forced_iterations + 1, use_modularity=use_modularity, max_cluster_size=max_cluster_size, seed=random_seed, ) return [ HierarchicalCluster.from_native(entry) for entry in hierarchical_clusters_native ]