Blind Inference of Eigenvector Centrality Rankings

We consider the problem of estimating a network's eigenvector centrality only from data on the nodes, with no information about network topology. Leveraging the versatility of graph filters to model network processes, data supported on the nodes is modeled as a graph signal obtained via the output of a graph filter applied to white noise. We seek to simplify the downstream task of centrality ranking by bypassing network topology inference methods and, instead, inferring the centrality structure of the graph directly from the graph signals. To this end, we propose two simple algorithms for ranking a set of nodes connected by an unobserved set of edges. We derive asymptotic and non-asymptotic guarantees for these algorithms, revealing key features that determine the complexity of the task at hand. Finally, we illustrate the behavior of the proposed algorithms on synthetic and real-world datasets.

I. Introduction

As Relational, non-Euclidean data has become increasingly prominent, so has the need for algorithms to make sense of arbitrarily structured datasets. The representation of data as graphs, or networks, is a popular approach [2]–[4], allowing one to uncover community structure [5], common connection patterns [6], and node importance [7].