高阶网络统计指标综述

Fundamental statistics of higher-order networks:a survey

复杂网络是描述和理解现实世界中复杂系统的有力工具.近年来,为了更准确地描述复杂网络中的交互关系,或者从高阶视角分析成对交互作用网络,许多学者开始使用高阶网络进行建模,并在研究其动力学过程中发现了与成对交互作用网络不同的新现象.然而,与成对交互作用网络相比,高阶网络的研究相对较少;而且,高阶网络结构相对复杂,基于结构的统计指标定义较为分散且形式不统一,这些都给描述高阶网络的拓扑结构特征带来了困难.鉴于此,本文综述了两种最常见的高阶网络——超图和单纯形网络——常用的统计指标及其物理意义.本文有助于加深对高阶网络的理解,促进对高阶网络结构特征的定量化研究,也有助于研究者在此基础上开发更多适用于高阶网络的统计指标.

Complex networks serve as indispensable instruments for characterizing and understanding intricate realworld systems.Recently,researchers have delved into the realm of higher-order networks,seeking to delineate interactions within these networks with greater precision or analyze traditional pairwise networks from a higherdimensional perspective.This effort has unearthed some new phenomena different from those observed in the traditional pairwise networks.However,despite the importance of higher-order networks,research in this area is still in its infancy.In addition,the complexity of higher-order interactions and the lack of standardized definitions for structure-based statistical indicators,also pose challenges to the investigation of higher-order networks.In recognition of these challenges,this paper presents a comprehensive survey of commonly employed statistics and their underlying physical significance in two prevalent types of higher-order networks:hypergraphs and simplicial complex networks.This paper not only outlines the specific calculation methods and application scenarios of these statistical indicators,but also provides a glimpse into future research trends.This comprehensive overview serves as a valuable resource for beginners or cross-disciplinary researchers interested in higher-order networks,enabling them to swiftly grasp the fundamental statistics pertaining to these advanced structures.By promoting a deeper understanding of higher-order networks,this paper facilitates quantitative analysis of their structural characteristics and provides guidance for researchers who aim to develop new statistical methods for higher-order networks.