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