networksns.centrality_measures.total_communicability

networksns.centrality_measures.total_communicability(G, t=1)

Computes the total communicability of all the nodes of a graph \(G\).

Total communicability is defined as the row sums of the exponential of the adjacency matrix [1], so denoting with \(A\) the adjacency matrix of graph \(G\) and with \(\mathbf{1}\) the vector of all ones, we have \(tc= e^{tA} \mathbf{1}\).

Parameters:

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

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

Returns:

tc (dict) total communicability of all the nodes of \(G\).

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 \(tc= e^A \mathbf{1}\).

>>>    tc = cm.total_communicability(G)

References