Preferential attachment hypergraph with high modularity

TL;DR

This paper introduces a dynamic preferential attachment hypergraph model that captures real-world network properties like power-law degree distribution and high modularity, improving upon existing models for hypergraph generation.

Contribution

The paper presents a novel hypergraph model combining preferential attachment with community structure, and provides theoretical analysis and empirical validation.

Findings

Degree distribution follows a power-law

Model achieves high modularity

Performs well on real-world co-authorship data

Abstract

Numerous works have been proposed to generate random graphs preserving the same properties as real-life large scale networks. However, many real networks are better represented by hypergraphs. Few models for generating random hypergraphs exist and no general model allows to both preserve a power-law degree distribution and a high modularity indicating the presence of communities. We present a dynamic preferential attachment hypergraph model which features partition into communities. We prove that its degree distribution follows a power-law and we give theoretical lower bounds for its modularity. We compare its characteristics with a real-life co-authorship network and show that our model achieves good performances. We believe that our hypergraph model will be an interesting tool that may be used in many research domains in order to reflect better real-life phenomena.