Percolation transition and distribution of connected components in generalized random network ensembles

TL;DR

This paper investigates the percolation transition and cluster distribution in generalized random network ensembles with complex structures, revealing a phase transition crossover influenced by network heterogeneity.

Contribution

It introduces a mapping of the network percolation problem to a Potts model with heterogeneous couplings, uncovering a phase transition crossover from second to first order.

Findings

Cluster distribution characterized by a Potts model mapping

Crossover from second to first order phase transition at q_c=2

Insights into dynamical processes on complex networks

Abstract

In this work, we study the percolation transition and large deviation properties of generalized canonical network ensembles. This new type of random networks might have a very rich complex structure, including high heterogeneous degree sequences, non-trivial community structure or specific spatial dependence of the link probability for networks embedded in a metric space. We find the cluster distribution of the networks in these ensembles by mapping the problem to a fully connected Potts model with heterogeneous couplings. We show that the nature of the Potts model phase transition, linked to the birth of a giant component, has a crossover from second to first order when the number of critical colors $q_c = 2$ in all the networks under study. These results shed light on the properties of dynamical processes defined on these network ensembles.