ash_model.measures.s_eigenvector_centrality

ash_model.measures.s_eigenvector_centrality(h, s, start=None, end=None, edges=True, max_iter=100, tol=1e-06, weight=None)[source]

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

  • max_iter (int) – maximum number of iterations for the eigenvector centrality calculation

  • tol (float) – tolerance for convergence in the eigenvector centrality calculation

  • weight – edge attribute to use as weight

Returns:

a dictionary mapping node IDs (or edge IDs if edges is True) to their eigenvector 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_eigenvector_centrality(h, 1, start=0, end=0).items()))[:3]
>>> [(k, float(v)) for k,v in head3]
[('e1', 0.12621433668406887), ('e10', 0.1777592407633311), ('e100', 0.010063200782658498)]