|*^c@sddZddlZdjdddgZddgZd d dd d Zd d ZdZ dS(s Eigenvector centrality. iNs s%Aric Hagberg (aric.hagberg@gmail.com)sPieter Swart (swart@lanl.gov)s#Sasha Gutfraind (ag362@cornell.edu)teigenvector_centralityteigenvector_centrality_numpyidgư>tweightc Cs5ddlm}t|tjks:t|tjkrLtjdnt|dkrptjdn|d krt g|D]}|dt|f^q}n|}dt |j }x|D]} || c|9||D]2} || c| |||| j|d7>> 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'] See Also -------- eigenvector_centrality_numpy pagerank hits Notes ----- The measure was introduced by [1]_. 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" eigenvector centrality which corresponds to the in-edges in the graph. For out-edges eigenvector centrality first reverse the graph with ``G.reverse()``. References ---------- .. [1] 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 .. [2] Mark E. J. Newman: Networks: An Introduction. Oxford University Press, USA, 2010, pp. 169. i(tsqrtsNot defined for multigraphs.is Empty graph.g?icss|]}|dVqdS(iN((t.0tv((s~/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/centrality/eigenvector.pys yssVeigenvector_centrality(): power iteration failed to converge in %d iterations."%(i+1))N(tmathRttypetnxt MultiGrapht MultiDiGraphtNetworkXExceptiontlentNonetdicttsumtvaluestnumber_of_nodestrangetfromkeystgettZeroDivisionErrortabst NetworkXError(tGtmax_iterttoltnstartRRtntxtstktnnodestitxlasttnbrterr((s~/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/centrality/eigenvector.pyRs:L* 2   4*   1c Csddl}ddlm}t|dkr@tjdntj|d|jd|dt}|j |j d d d d \}}|j j }|j |j|jj|}tt|tt||} | S( sCompute 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 `i` is .. math:: \mathbf{Ax} = \lambda \mathbf{x} where `A` is the adjacency matrix of the graph G with eigenvalue `\lambda`. By virtue of the Perron–Frobenius theorem, there is a unique and positive solution if `\lambda` is the largest eigenvalue associated with the eigenvector of the adjacency matrix `A` ([2]_). Parameters ---------- G : graph A networkx graph weight : None or string, optional The name of the edge attribute used as weight. If None, all edge weights are considered equal. Returns ------- nodes : dictionary Dictionary of nodes with eigenvector centrality as the value. Examples -------- >>> G = nx.path_graph(4) >>> centrality = nx.eigenvector_centrality_numpy(G) >>> print(['%s %0.2f'%(node,centrality[node]) for node in centrality]) ['0 0.37', '1 0.60', '2 0.60', '3 0.37'] See Also -------- eigenvector_centrality pagerank hits Notes ----- The measure was introduced by [1]_. This algorithm uses the SciPy sparse eigenvalue solver (ARPACK) to find the largest eigenvalue/eigenvector pair. For directed graphs this is "left" eigenvector centrality which corresponds to the in-edges in the graph. For out-edges eigenvector centrality first reverse the graph with G.reverse(). References ---------- .. [1] 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 .. [2] Mark E. J. Newman: Networks: An Introduction. Oxford University Press, USA, 2010, pp. 169. iN(tlinalgis Empty graph.tnodelistRtdtypeRitwhichtLR(tscipyt scipy.sparseR%R RR tto_scipy_sparse_matrixtnodestfloatteigstTtflattentrealtsignRtnormRtziptmap( RRtspR%tMt eigenvaluet eigenvectortlargestR4t centrality((s~/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/centrality/eigenvector.pyRs?  $%"cCs:ddlm}yddl}Wn|dnXdS(Ni(tSkipTestsSciPy not available(tnoseR=R*(tmoduleR=R*((s~/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/centrality/eigenvector.pyt setup_modules ( t__doc__tnetworkxRtjoint __author__t__all__R RRR@(((s~/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/centrality/eigenvector.pyts      u M