Bond percolation on a class of correlated and clustered random graphs

TL;DR

This paper develops a formalism to analyze bond percolation in complex, correlated, and clustered random graphs, extending the Configuration Model to include hyperedges and multiple node types, enabling better modeling of real networks.

Contribution

It introduces a multitype, hyperedge-based formalism for bond percolation, capturing complex clustering and correlations in random graphs, advancing network modeling capabilities.

Findings

Reproduces a wide spectrum of complex network patterns

Highlights unusual behaviors in component sizes and composition

Demonstrates applicability on synthetic social networks

Abstract

We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the Configuration Model where nodes of different types are connected via different types of hyperedges, edges that can link more than 2 nodes. We argue that the multitype approach coupled with the use of clustered hyperedges can reproduce a wide spectrum of complex patterns, and thus enhances our capability to model real complex networks. As an illustration of this claim, we use our formalism to highlight unusual behaviors of the size and composition of the components (small and giant) in a synthetic, albeit realistic, social network.