Growing Hypergraphs with Preferential Linking

TL;DR

This paper introduces models of growing hypergraphs with preferential linking, analyzing how different growth rules influence degree and hyperedge size distributions, revealing that hyperedge-based growth alone can produce scale-free networks.

Contribution

It generalizes preferential-attachment models to hypergraphs and explores how hyperedge-based growth affects network degree and size distributions.

Findings

Hyperedge-based growth can produce power-law degree distributions without node-wise preferential attachment.

Hyperedge size distribution varies from exponential to power-law depending on growth rules.

Numerical simulations confirm theoretical predictions.

Abstract

A family of models of growing hypergraphs with preferential rules of new linking is introduced and studied. The model hypergraphs evolve via the hyperedge-based growth as well as the node-based one, thus generalizing the preferential-attachment models of scale-free networks. We obtain the degree distribution and hyperedge size distribution for various combinations of node- and hyperedge-based growth modes. We find that the introduction of hyperedge-based growth can give rise to power-law degree distribution $P(k)\sim k^{-\gamma}$ even without node-wise preferential-attachments. The hyperedge size distribution $P(s)$ can take diverse functional forms, ranging from exponential to power-law to a nonstationary one, depending on the specific hyperedge-based growth rule. Numerical simulations support the mean-field theoretical analytical predictions.