Percolation transition in correlated hypergraphs

TL;DR

This paper investigates how correlations influence the percolation threshold in random hypergraphs by modeling them with hidden variable ensembles and mapping the problem to a Potts model with heterogeneous couplings.

Contribution

It introduces a novel approach to analyze correlated hypergraphs using hidden variable ensembles and a Potts model mapping, advancing understanding of percolation in complex networks.

Findings

Correlations significantly affect the percolation threshold.

The hypergraph percolation problem can be mapped to a Potts model with heterogeneous couplings.

The method provides insights into the structure of correlated complex networks.

Abstract

Correlations are known to play a crucial role in determining the structure of complex networks. Here we study how their presence affects the computation of the percolation threshold in random hypergraphs. In order to mimic the correlation in real network, we build hypergraphs from a generalized hidden variable ensembles and we study the percolation transition by mapping this problem to the fully connected Potts model with heterogeneous couplings.