Structural Analysis of Viral Spreading Processes in Social and Communication Networks Using Egonets

TL;DR

This paper develops a mathematical framework to estimate the bounds of the largest eigenvalue of a network's adjacency matrix using local egonet data, aiding in understanding and controlling viral spreading in large networks.

Contribution

It introduces a novel algebraic and convex optimization-based method to bound the largest eigenvalue from egocentric network views, enabling analysis without full network data.

Findings

Local structural properties significantly constrain the largest eigenvalue.

The approach accurately estimates eigenvalue bounds from egonet collections.

Results can inform strategies for virus containment and information dissemination.

Abstract

We study how the behavior of viral spreading processes is influenced by local structural properties of the network over which they propagate. For a wide variety of spreading processes, the largest eigenvalue of the adjacency matrix of the network plays a key role on their global dynamical behavior. For many real-world large-scale networks, it is unfeasible to exactly retrieve the complete network structure to compute its largest eigenvalue. Instead, one usually have access to myopic, egocentric views of the network structure, also called egonets. In this paper, we propose a mathematical framework, based on algebraic graph theory and convex optimization, to study how local structural properties of the network constrain the interval of possible values in which the largest eigenvalue must lie. Based on this framework, we present a computationally efficient approach to find this interval from a collection of egonets. Our numerical simulations show that, for several social and communication networks, local structural properties of the network strongly constrain the location of the largest eigenvalue and the resulting spreading dynamics. From a practical point of view, our results can be used to dictate immunization strategies to tame the spreading of a virus, or to design network topologies that facilitate the spreading of information virally.