Blind Inference of Centrality Rankings from Graph Signals

TL;DR

This paper introduces a spectral algorithm to infer node centrality rankings from graph signals without knowing the network topology, providing theoretical performance bounds and empirical validation.

Contribution

It presents a novel method for blind centrality ranking from signals, with finite sample analysis and application to dense ER graphs.

Findings

Algorithm accurately ranks nodes in synthetic networks.

Performance depends on network density and signal quantity.

Theoretical bounds guide the number of signals needed.

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 \ER 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.