Nonmonotonic percolation threshold in correlated networks and hypergraphs

TL;DR

This paper investigates how assortative and disassortative mixing influence network robustness, revealing nonmonotonic relationships between correlation and percolation thresholds in networks and hypergraphs.

Contribution

It uncovers nonmonotonic effects of degree correlations on network and hypergraph robustness, extending analysis beyond simple networks to hypergraphs.

Findings

Moderately disassortative networks can be more fragile than strongly disassortative or uncorrelated ones.

Positively correlated hypergraphs tend to be more fragile than negatively correlated ones.

The relationship between assortativity and percolation threshold is nonmonotonic in both networks and hypergraphs.

Abstract

We study the effect of assortative and disassortative mixing on the robustness of networks under random node failures. For ordinary (dyadic) networks, by using the generating function technique and stochastic simulations, we show that the relationship between the Pearson assortativity coefficient $r$ and the percolation threshold $p_c$ is not always monotonic. More specifically, in certain regions of the parameter space of our model, moderately disassortative networks can be more fragile than either strongly disassortative or uncorrelated networks. We observe this nonmonotonic behavior for trimodal networks as well as for networks with Poisson and power-law degree distributions. We then extend our analysis to hypergraphs with correlations between node hyperdegree and hyperedge cardinality. For this case, we find that positively correlated hypergraphs tend to be more fragile than negatively correlated ones. Additionally, as in the dyadic case, the relationship between $r$ and $p_c$ is nonmonotonic, and the most fragile configuration does not correspond to the most assortative hypergraph.