← 研踪 PaperTrailarXiv:2611.15313 · v1
Influence of Assortativity on the SICP Spreading Process in Hypergraphs
首次提交 2026-11-11 18:49
版本更新 2026-11-11 18:49
雷达观测 2026-11-13 11:11
摘要
Many real-world systems involve group interactions that cannot be captured by pairwise graphs. They can be better represented by hypergraphs where each hyperedge could connect an arbitrary number of nodes. The Susceptible-Infected Contact Process (SICP) has been proposed to model the spreading of information and epidemics on hypergraphs. However, how higher-order topological properties of a hypergraph influence the SICP spreading process remains understudied. In this paper, we examine the impact of hypergraph assortativity based on the Neighborhood Coefficient (NC)-the average size of hyperedges incident to a node-on the SICP spreading process. By introducing a low-complexity measure of hypergraph assortativity grounded in analysis of variance, we apply hyperdegree-preserving rewirings to real-world networks and synthetic hypergraph models to tune their assortativity. We find and explain why lower NC assortativity yields higher average epidemic prevalence and lower prevalence variance across different seed selections. This phenomenon is evident when hyperdegree-preserving rewirings are applied to real-world networks with heterogeneous topological structures, but it is largely absent when comparing synthetic random hypergraphs to their rewired counterparts.
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v1 · 2026-11-11 18:49 · 最新观测版本
Influence of Assortativity on the SICP Spreading Process in Hypergraphs
Many real-world systems involve group interactions that cannot be captured by pairwise graphs. They can be better represented by hypergraphs where each hyperedge could connect an arbitrary number of nodes. The Susceptible-Infected Contact Process (SICP) has been proposed to model the spreading of information and epidemics on hypergraphs. However, how higher-order topological properties of a hypergraph influence the SICP spreading process remains understudied. In this paper, we examine the impact of hypergraph assortativity based on the Neighborhood Coefficient (NC)-the average size of hyperedges incident to a node-on the SICP spreading process. By introducing a low-complexity measure of hypergraph assortativity grounded in analysis of variance, we apply hyperdegree-preserving rewirings to real-world networks and synthetic hypergraph models to tune their assortativity. We find and explain why lower NC assortativity yields higher average epidemic prevalence and lower prevalence variance across different seed selections. This phenomenon is evident when hyperdegree-preserving rewirings are applied to real-world networks with heterogeneous topological structures, but it is largely absent when comparing synthetic random hypergraphs to their rewired counterparts.
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