Motif-based mean-field approximation of interacting particles on clustered networks

TL;DR

This paper introduces a motif-based mean-field approximation for interacting particles on clustered networks, capturing higher-order structures to improve accuracy over traditional degree-based methods.

Contribution

It presents a novel mean-field approach that incorporates motifs, enabling better modeling of dynamics on clustered networks compared to existing cluster-free approximations.

Findings

Numerical results show close agreement with stochastic simulations.

Existing methods fail to accurately predict dynamics on clustered networks.

The approach effectively captures higher-order subgraph effects.

Abstract

Interacting particles on graphs are routinely used to study magnetic behaviour in physics, disease spread in epidemiology, and opinion dynamics in social sciences. The literature on mean-field approximations of such systems for large graphs is limited to cluster-free graphs for which standard approximations based on degrees and pairs are often reasonably accurate. Here, we propose a motif-based mean-field approximation that considers higher-order subgraph structures in large clustered graphs. Numerically, our equations agree with stochastic simulations where existing methods fail.