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This paper characterizes the difficulty of estimating a network's eigenvectorcentrality only from data on the nodes, i.e., with no information about thetopology of the network. We model this nodal data as graph signals generated bypassing white noise through generic (not necessarily low-pass) graph filters.Leveraging the spectral properties of graph filters, we estimate theeigenvectors of the adjacency matrix of the underlying network. To this end, asimple selection algorithm is proposed, which chooses the correct eigenvectorof the signal covariance matrix with minimal assumptions on the underlyinggraph filter. We then present a theoretical characterization of the asymptoticand non-asymptotic performance of this algorithm, thus providing a samplecomplexity bound for the centrality estimation and revealing key elementsdriving this complexity. Finally, we illustrate the developed insights througha set of numerical experiments on different random graph models.

Blind Estimation of Eigenvector Centrality from Graph Signals: Beyond Low-pass Filtering