Spectral Analysis of Virus Spreading in Random Geometric Networks

TL;DR

This paper analyzes how virus spreads in random geometric networks by examining the eigenvalues of their adjacency matrices, providing explicit formulas and conditions to control infections.

Contribution

It introduces new explicit expressions for eigenvalue moments of RGGs and derives an analytical condition to mitigate viral spread in such networks.

Findings

Eigenvalue moments depend on node density and connection radius.

Analytical condition for controlling viral spread in RGGs.

Numerical simulations confirm theoretical predictions.

Abstract

In this paper, we study the dynamics of a viral spreading process in random geometric graphs (RGG). The spreading of the viral process we consider in this paper is closely related with the eigenvalues of the adjacency matrix of the graph. We deduce new explicit expressions for all the moments of the eigenvalue distribution of the adjacency matrix as a function of the spatial density of nodes and the radius of connection. We apply these expressions to study the behavior of the viral infection in an RGG. Based on our results, we deduce an analytical condition that can be used to design RGG's in order to tame an initial viral infection. Numerical simulations are in accordance with our analytical predictions.