On the accuracy of population level approximation of network processes

TL;DR

This paper evaluates how accurately population-level models approximate the transient dynamics of simple contagion processes on regular graphs, providing theoretical estimates and numerical validation.

Contribution

It offers a theoretical estimate of the approximation accuracy for simple contagion processes on regular graphs, especially Turán graphs, including numerical validation.

Findings

Theoretical estimates are sharp for dense graphs.

Population-level approximation effectively captures transient behavior.

Numerical results support the theoretical bounds.

Abstract

The individual-based model of simple contagion processes is considered on regular graphs. This model explicitly incorporates the adjacency matrix of the network enabling us to study the effect of network structure on the dynamic of the propagation process. While the asymptotic behaviour of the model is well known, the transient behaviour has been less studied. Our goal in this paper is to give a theoretical estimate on the accuracy of the one-dimensional population-level approximation. This is carried out for arbitrary simple contagion processes and regular Tur\'an graphs. Numerical evidence is shown that the theoretical estimate is rather sharp for dense graphs.