发表机构
School of Computer Science, University of St Andrews（圣安德鲁斯大学计算机学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于块图的网络演化模型，通过添加m-团和删除顶点，推导出联合度分布主方程的精确闭式解，并利用年龄分辨消息传递获得巨连通分量和渗流阈值，推广了现有模型至任意更替率。
AI 中文摘要
演化网络通过随时间发生的顶点添加和删除过程而演变，这些过程塑造了它们的结构和功能。在许多实证网络中，顶点并非孤立地到达或离开，而是以群体或队列的形式出现：例如，合著网络通过每当发表一篇有多位作者的新论文时添加团（完全连通子图）而增长。在本文中，我们提出一个基于块图的随机网络演化模型，该模型通过添加完全连通子图（$m$-团）和删除单个顶点来演化。我们推导出控制联合度分布时间演化的主方程，并获得一个精确的闭式解，该解在均匀附着下对任意顶点删除率均有效，并描述了增长网络和恒定规模网络。由此解，我们得到边缘度分布和聚类系数的闭式表达式，以及使用年龄分辨消息传递得到的巨连通分量大小和决定对随机顶点故障鲁棒性的渗流阈值。我们的结果将现有的单顶点添加-删除模型推广到任意更替率下基于团的动力学，并得到蒙特卡洛模拟的证实。
英文摘要
Evolving networks experience vertex addition and deletion over time via processes which shape their structure and function. In many empirical networks, vertices do not arrive or depart in isolation but instead within groups or cohorts: for example, coauthorship networks grow by the addition of cliques whenever a new paper with multiple authors is published. In this paper, we propose a stochastic network evolution model based on block graphs that evolve through the addition of fully connected subgraphs ($m$-cliques) and the deletion of individual vertices. We derive a master equation governing the time evolution of the joint degree distribution and obtain an exact closed-form solution, valid for an arbitrary vertex deletion rate under uniform attachment, that describes both growing and constant-size networks. From this solution we obtain the marginal degree distributions and the clustering coefficient in closed form and the size of the giant connected component and percolation threshold governing robustness to random vertex failure using age-resolved message passing. Our results generalise existing single-vertex addition-deletion models to clique-based dynamics at arbitrary rates of turnover, and are confirmed by Monte Carlo simulation.
Comments28 pages, 8 figures
