一般有向超图上的高阶富俱乐部与构型模型
Higher-order rich clubs and configuration models on general directed hypergraphs
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中文总结 AI 辅助
本文针对一般有向超图提出超富俱乐部流程，统一多种有向超图概念，可检测标准图富俱乐部遗漏的各类网络中有意义的高阶结构。
中文摘要 AI 辅助
检测复杂网络（尤其是来自物理系统的网络）中的结构是科学领域的核心问题之一，一种方法是通过富俱乐部分析，该方法利用中心性指标识别重要顶点，并衡量这些顶点是否比随机预期更紧密地相互连接。尽管富俱乐部分析具有参考价值，但它仅能捕捉成对相互作用，而忽略了已知会影响许多复杂系统结构与功能的高阶相互作用。本文提出了一种超富俱乐部流程，该流程通过编码高阶相互作用的超边来衡量中心顶点是否比随机预期更紧密地相互连接，同时还能纳入常被忽略的重要方向信息。本文所研究的超图属于一类广义的一般有向超图，其特殊情形包括无向超图、头尾有向超图以及全序超图（一种与拓扑数据分析中有向单纯复形相关的超图），该定义将几种非等价的有向超图概念统一在同一框架下。本文在这类超图上定义了超富俱乐部框架，其具体构造依赖于领域科学家根据研究目标确定的明确选择，特定选择可还原图和无向超图的现有富俱乐部概念，还为各类有向超图分别提出了首个此类概念。本文通过研究不同来源的网络（连接组、传染病传播时间网络、诗歌网络以及XGI超图数据库）验证了该流程能恢复数据中有意义的结构，且在每种情况下都检测到了标准图富俱乐部未能捕捉到的结构。
英文摘要
Detecting structure in complex networks, especially those arising from physical systems, is a central problem across the sciences. One approach is via rich club analysis, which identifies important vertices using a centrality metric and measures whether those vertices are more tightly interconnected than expected by chance. While informative, this approach captures only pairwise interactions, missing out on higher-order ones known to shape the structure and function of many complex systems. We propose a hyper-rich club pipeline that asks whether central vertices are more tightly interconnected than expected by chance through hyperedges encoding higher-order interactions, which also enables the inclusion of important, often omitted, directional information. We work in a broad class of hypergraphs, which we call general directed hypergraphs, that includes as special cases undirected hypergraphs, head-and-tail directed hypergraphs, and totally ordered hypergraphs (a hypergraph related to directed simplicial complexes from topological data analysis). This unifies several non-equivalent notions of directed hypergraph under one definition. On these hypergraphs we define a hyper-rich club framework whose concrete construction depends on explicit choices the domain scientist fixes according to their research goals. Particular choices recover the existing rich club notions for graphs and undirected hypergraphs, and yield the first such notion for each version of directed hypergraphs. We demonstrate that the pipeline recovers meaningful structure in data by studying networks of very different origins: connectomes, temporal networks of infectious spread, networks of poems, and the XGI hypergraph database, in each case detecting structure the standard graph rich club misses.
发表机构
- Nottingham Trent University（诺丁汉特伦特大学）
- Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克科学计量学研究所）
- Institute of Clinical and Preventive Medicine, University of Latvia（拉脱维亚大学临床与预防医学研究所）
- Graz University of Technology（格拉茨工业大学）
- Computer and Information Sciences, University of Strathclyde（思克莱德大学计算机与信息科学学院）
- Max Planck Institute of Molecular Cell Biology and Genetics (MPI-CBG)（马克斯·普朗克分子细胞生物学与遗传学研究所）
- Center for Systems Biology Dresden (CSBD)（德累斯顿系统生物学中心）
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