78 lines
2.4 KiB
Python
78 lines
2.4 KiB
Python
from collections import defaultdict
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import networkx as nx
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__all__ = ["k_clique_communities"]
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def k_clique_communities(G, k, cliques=None):
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"""Find k-clique communities in graph using the percolation method.
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A k-clique community is the union of all cliques of size k that
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can be reached through adjacent (sharing k-1 nodes) k-cliques.
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Parameters
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----------
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G : NetworkX graph
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k : int
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Size of smallest clique
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cliques: list or generator
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Precomputed cliques (use networkx.find_cliques(G))
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Returns
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-------
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Yields sets of nodes, one for each k-clique community.
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Examples
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--------
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>>> from networkx.algorithms.community import k_clique_communities
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>>> G = nx.complete_graph(5)
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>>> K5 = nx.convert_node_labels_to_integers(G, first_label=2)
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>>> G.add_edges_from(K5.edges())
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>>> c = list(k_clique_communities(G, 4))
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>>> sorted(list(c[0]))
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[0, 1, 2, 3, 4, 5, 6]
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>>> list(k_clique_communities(G, 6))
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[]
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References
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----------
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.. [1] Gergely Palla, Imre Derényi, Illés Farkas1, and Tamás Vicsek,
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Uncovering the overlapping community structure of complex networks
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in nature and society Nature 435, 814-818, 2005,
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doi:10.1038/nature03607
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"""
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if k < 2:
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raise nx.NetworkXError(f"k={k}, k must be greater than 1.")
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if cliques is None:
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cliques = nx.find_cliques(G)
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cliques = [frozenset(c) for c in cliques if len(c) >= k]
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# First index which nodes are in which cliques
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membership_dict = defaultdict(list)
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for clique in cliques:
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for node in clique:
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membership_dict[node].append(clique)
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# For each clique, see which adjacent cliques percolate
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perc_graph = nx.Graph()
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perc_graph.add_nodes_from(cliques)
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for clique in cliques:
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for adj_clique in _get_adjacent_cliques(clique, membership_dict):
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if len(clique.intersection(adj_clique)) >= (k - 1):
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perc_graph.add_edge(clique, adj_clique)
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# Connected components of clique graph with perc edges
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# are the percolated cliques
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for component in nx.connected_components(perc_graph):
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yield (frozenset.union(*component))
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def _get_adjacent_cliques(clique, membership_dict):
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adjacent_cliques = set()
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for n in clique:
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for adj_clique in membership_dict[n]:
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if clique != adj_clique:
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adjacent_cliques.add(adj_clique)
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return adjacent_cliques
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