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eigenvector_centrality(G, max_iter=100, tol=1e-06, nstart=None, weight='weight')¶
Compute the eigenvector centrality for the graph G.
Eigenvector centrality computes the centrality for a node based on the centrality of its neighbors. The eigenvector centrality for node is
where is the adjacency matrix of the graph G with eigenvalue . By virtue of the Perron–Frobenius theorem, there is a unique and positive solution if is the largest eigenvalue associated with the eigenvector of the adjacency matrix ().
- G (graph) – A networkx graph
- max_iter (integer, 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.
nodes – Dictionary of nodes with eigenvector centrality as the value.
>>> 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']
 Phillip Bonacich: Power and Centrality: A Family of Measures. American Journal of Sociology 92(5):1170–1182, 1986 http://www.leonidzhukov.net/hse/2014/socialnetworks/papers/Bonacich-Centrality.pdf  Mark E. J. Newman: Networks: An Introduction. Oxford University Press, USA, 2010, pp. 169.