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eigenvector_centrality(G, max_iter=100, tol=1e-06, nstart=None)

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.

Returns :

nodes : dictionary

Dictionary of nodes with eigenvector centrality as the value.

See also

eigenvector_centrality_numpy, pagerank, hits


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 “right” eigevector centrality. For “left” eigenvector centrality, first reverse the graph with G.reverse().


>>> 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']