ash_model.measures.s_second_order_centrality

ash_model.measures.s_second_order_centrality(h, s, start=None, end=None, edges=True)[source]

Returns the second-order centrality of the nodes in the line graph of the hypergraph. If edges is True, the function computes the second-order centrality for hyperedges (the nodes of the line graph). If edges is False, it computes the second-order 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

Returns:

a dictionary mapping node IDs (or edge IDs if edges is True) to their second-order 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_second_order_centrality(h, 1, start=0, end=0).items()))[:3]
>>> head3
[('e1', 373.1451853808109), ('e10', 226.34942005127067), ('e100', 687.213714885934)]