eigenvector_centrality¶

eigenvector_centrality(G, max_iter=100, tol=1e-06, nstart=None, weight='weight')[source]¶

Compute the eigenvector centrality for the graph G.

Uses the power method to find the eigenvector for the largest eigenvalue of the adjacency matrix of G.

Parameters:

G : graph A networkx graph max_iter : interger, optional Maximum number of iterations in power method. tol : float, optional Error tolerance used to check convergence in power method iteration. nstart : dictionary, optional Starting value of eigenvector iteration for each node. weight : None or string, optional If None, all edge weights are considered equal. Otherwise holds the name of the edge attribute used as weight.

Returns:

nodes : dictionary Dictionary of nodes with eigenvector centrality as the value.

See also

eigenvector_centrality_numpy, pagerank, hits

Notes

The eigenvector calculation is done by the power iteration method and has no guarantee of convergence. The iteration will stop after max_iter iterations or an error tolerance of number_of_nodes(G)*tol has been reached.

For directed graphs this is “left” eigevector centrality which corresponds to the in-edges in the graph. For out-edges eigenvector centrality first reverse the graph with G.reverse().

Examples

>>> G = nx.path_graph(4)
>>> centrality = nx.eigenvector_centrality(G)
>>> print(['%s %0.2f'%(node,centrality[node]) for node in centrality])
['0 0.37', '1 0.60', '2 0.60', '3 0.37']