Dynamics on Modular Networks with Heterogeneous Correlations

TL;DR

This paper introduces a new modular network model with heterogeneous degree correlations, providing an analytical framework to study various binary dynamics like percolation and threshold models on such complex structures.

Contribution

It develops a generalized ensemble of modular networks with module-specific degree correlations, extending existing models and enabling analysis of diverse dynamics.

Findings

Analytical approach for binary dynamics on modular networks

Model captures heterogeneous degree correlations across modules

Applicable to nonidentical interacting networks

Abstract

We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules. We present an analytical approach that allows one to analyze several types of binary dynamics operating on such networks, and we illustrate our approach using bond percolation, site percolation, and the Watts threshold model. The new network ensemble generalizes existing models (e.g., the well-known configuration model and LFR networks) by allowing a heterogeneous distribution of degree-degree correlations across modules, which is important for the consideration of nonidentical interacting networks.