A1395
Title: Preferential attachment hypergraph model with randomized hyperedge count and size
Authors: Hohyun Jung - Sungshin Women's University (Korea, South)
Frederick Kin Hing Phoa - Academia Sinica (Taiwan) [presenting]
Sung-Ho Kim - KAIST (Korea, South)
Abstract: Hypergraphs provide a natural framework for modeling higher-order interactions among nodes, with real-world hypergraph data often exhibiting weighted and heterogeneous structures. A preferential attachment hypergraph model is proposed that incorporates randomness in two key components: the number of hyperedges a node connects to upon arrival, and the size of each hyperedge. By allowing these quantities to follow arbitrary probability distributions, the model generalizes prior fixed-parameter settings and better reflects empirical observations. The asymptotic degree distribution is analytically derived under mild assumptions, showing that it follows a power-law whose exponent is governed by the distribution of hyperedge sizes. Moreover, the distribution of hyperedge counts significantly influences the degree behavior in the small-degree regime, where deviations from ideal power-law patterns are often seen in real-world networks. The overall degree distribution can be expressed as a mixture of fixed-count degree distributions. Simulation results and real data analyses support the theoretical findings and highlight the practical relevance of the proposed model.
