Emergence of coexisting percolating clusters in networks

TL;DR

This paper introduces sausage-like networks (SLNs) where multiple percolating clusters can coexist, challenging traditional assumptions, and develops a modular message passing approach to accurately describe this phenomenon, improving predictions for network robustness and epidemic modeling.

Contribution

The paper presents the concept of coexisting percolating clusters in modular networks and introduces the modular message passing method to better predict percolation behavior.

Findings

Coexisting percolating clusters emerge due to limited inter-module links.

MMP significantly improves percolation predictions over traditional message passing.

Findings impact understanding of network robustness and epidemic spread modeling.

Abstract

It is commonly assumed in percolation theories that at most one percolating cluster can exist in a network. We introduce sausage-like networks (SLNs), an ensemble of synthetic modular networks in which more than one percolating cluster can appear. We show that coexisting percolating clusters (CPCs) emerge in such networks due to limited mixing, i.e., a small number of interlinks between pairs of modules. We develop an approach called modular message passing (MMP) to describe and verify these observations. We demonstrate that the appearance of CPCs is an important source of inaccuracy in the previously introduced percolation theories, such as the message passing (MP) approach. Moreover, we show that the MMP theory improves significantly over the predictions of MP for percolation on synthetic networks with limited mixing and also on several real-world networks. These findings have important implications for understanding the robustness of networks and in quantifying epidemic outbreaks in the susceptible-infected-recovered (SIR) model of disease spread.