networksns.centrality_measures.subgraph_centrality

networksns.centrality_measures.subgraph_centrality(G, t=1, tol=1e-07, maxit=50)

Computes the subgraph centrality of all the nodes in graph \(G\).

The subgraph centrality of the \(i^{th}\) node is given by \([e^{tA}]_{ii}=e_i^T (e^{tA})e_i\), where \(e_i\) and \(A\) denote respectively the \(i^{th}\) vector of the canonical basis and the adjacency matrix of the graph [1].

Parameters:

  • G (Graph or DiGraph object) – a graph.

  • t (scalar, optional) – when exponentiating multiply the adjacency matrix by t, default: 1.

  • tol (float,optional) – tolerance for convergence, relative accuracy, default: 1e-7.

  • maxit (integer, optional) – maximum number of Lanczos iterations, default: 50.

Returns:

sc (dict) subgraph centrality of all nodes in \(G\).

Examples

>>>  from networksns import centrality_measures as cm
>>>  import networkx as nx

Create graph \(G\).

>>>    G = nx.Graph()
>>>    G.add_edge(1, 2)
>>>    G.add_edge(2, 3)
       EdgeView([(1, 2), (2, 3)])

Compute the subgraph centrality.

>>>    sc = cm.subgraph_centrality(G)

References