ash_model.measures.s_betweenness_centrality

ash_model.measures.s_betweenness_centrality(h, s, start=None, end=None, edges=True, normalized=True, weight=False)[source]

Returns the betweenness centrality of the nodes in the line graph of the hypergraph. If edges is True, the function computes the betweenness centrality for hyperedges (the nodes of the line graph). If edges is False, it computes the betweenness centrality for nodes by first converting the hypergraph to its dual.

Parameters:

  • h (ASH) – the ASH instance

  • s (int) – minimum hyperedge overlap size for paths

  • start (int | None) – start time of the interval

  • end (int | None) – end time of the interval

  • edges (bool) – if True, compute for hyperedges; if False, compute for nodes

  • normalized (bool) – if True, normalize the betweenness centrality values

  • weight (bool) – if True, use edge weights for the betweenness centrality calculation

Returns:

a dictionary mapping node IDs (or edge IDs if edges is True) to their betweenness centrality values

Return type:

dict

Examples

>>> import numpy as np, networkx as nx
>>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list
>>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)]
>>> rng = np.random.default_rng(42)
>>> for G in Gs:
...     for n in G.nodes():
...         G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue'
>>> h = from_networkx_maximal_cliques_list(Gs)
>>> head3 = sorted(list(s_betweenness_centrality(h, 1, start=0, end=0).items()))[:3]
>>> head3
[('e1', 0.0), ('e10', 0.021109461571662495), ('e100', 0.0035032472389105243)]