Blind Inference of Centrality Rankings from Graph Signals

Abstract

We study the blind centrality ranking problem, where our goal is to infer the eigenvector centrality ranking of nodes solely from nodal observations, i.e., without information about the topology of the network. We formalize these nodal observations as graph signals and model them as the outputs of a network process on the underlying (unobserved) network. A simple spectral algorithm is proposed to estimate the leading eigenvector of the associated adjacency matrix, thus serving as a proxy for the centrality ranking. A finite rate performance analysis of the algorithm is provided, where we find a lower bound on the number of graph signals needed to correctly rank (with high probability) two nodes of interest. We then specialize our general analysis for the particular case of dense Erdős-Rényi graphs, where existing graph-theoretical results can be leveraged. Finally, we illustrate the proposed algorithm via numerical experiments in synthetic and real-world networks, making special emphasis on how the network features influence the performance.

Provably Fast Asynchronous And Distributed Algorithms For Pagerank Centrality Computation

“…In this section, we overview the convergence properties of the SAbased PageRank algorithms. We first present a sublinear convergence result for the general case (8). Then, we show that by exploiting structure and using a recent result on the product of random matrices, the linear SA scheme converges with a linear rate in the special case with fixed topology [cf.…”

“…We borrow [19,Proposition 7] to analyze the convergence of linear SA (8) in the general case with diminishing step size α k : Theorem 1 Consider the linear SA scheme (8). Assume H1 and the step sizes satisfy α k ≤ α k+1 (1 + (m/8)α k+1 ) and sup k α k ≤ α∞ for some small α∞, then it holds for any k ≥ 1 that…”

“…Among others, the eigen-centrality is a popular centrality measure which assigns high importance to nodes that are connected to other important nodes. Recent works [7,8] suggested methods to estimate eigen-centrality blindly by only observing the graph signals on the graph.…”

Sampling on networks: estimating spectral centrality measures and their impact in evaluating other relevant network measures

“…To the best of our knowledge, TCEC sampling (Ruggeri and De Bacco 2020) is one of the first theoretical attempts in estimating eigenvalue centrality, which goes beyond heuristics or empirical reasoning. A closely related problem is that of estimating eigenvector centrality without observing any edge but only signals on nodes (Roddenberry and Segarra 2019;He and Wai 2020). A different but related research direction is to question the stability of centrality measures under perturbations (Segarra and Ribeiro 2015;Han and Lee 2016;Murai and Yoshida 2019).…”

Identifying First-Order Lowpass Graph Signals Using Perron Frobenius Theorem

“…Our work is related to the recent developments in graph inference or learning which aim at learning the graph topology blindly This work is supported by CUHK Direct Grant #4055135. Emails: {yrhe,htwai}@se.cuhk.edu.hk [7,[10][11][12][13][14][15]. For instance, [10][11][12][13] infer topology from smooth graph signals which can be given by lowpass graph filtering, [7,14,15] consider blind inference of communities and centrality from lowpass graph signals; see [16,17].…”