How universal is the mean-field universality class for percolation in complex networks?

TL;DR

This paper provides an exact solution for site percolation in strongly clustered random graphs, revealing that degree distribution alone cannot determine universality classes due to the influence of clustering and correlations.

Contribution

It offers the first exact solution for percolation in clustered networks and compares it with mean-field predictions, highlighting the limitations of degree-based universality assumptions.

Findings

Degree heterogeneity and clustering significantly affect percolation thresholds.

Heterogeneous mean-field theory can mispredict critical exponents in realistic networks.

Structural features beyond degree distribution influence universality classes.

Abstract

Clustering and degree correlations are ubiquitous in real-world complex networks. Yet, understanding their role in critical phenomena remains a challenge for theoretical studies. Here, we provide the exact solution of site percolation in a model for strongly clustered random graphs, with many overlapping loops and heterogeneous degree distribution. We systematically compare the exact solution with heterogeneous mean-field predictions obtained from a treelike random rewiring of the network, which preserves only the degree sequence. Our results demonstrate a nontrivial interplay between degree heterogeneity, correlations and network topology, which can significantly alter both the percolation threshold and the critical exponents predicted by the heterogeneous mean-field. These findings reveal limitations of heterogeneous mean-field theory, demonstrating that the degree distribution alone is insufficient to determine universality classes in complex networks with realistic structural features.