论文标题
随机图与任意聚类及其应用
Random graphs with arbitrary clustering and their applications
论文作者
论文摘要
许多真实网络的结构不是本地树状的，因此网络分析无法表征其键渗透属性。在最近的一篇论文中[P. Mann，V。A. Smith，J。B. O. Mitchell和S. Dobson，在具有高阶聚类的随机图中渗透，Arxiv e-Prints，p。 ARXIV：2006.06744，2020年6月。]，我们开发了具有均匀聚类的随机网络的渗透特性的分析解决方案（其节点是等效的群集）。在本文中，我们将此模型扩展到了包含群集的网络，这些网络的节点不等于程度，包括多层网络。通过数值示例，我们展示了如何使用此方法来研究具有任意聚类的随机复杂网络的属性，从而扩展了配置模型的适用性并生成函数公式。
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in random graphs with higher-order clustering, arXiv e-prints, p. arXiv:2006.06744, June 2020.], we developed analytical solutions to the percolation properties of random networks with homogeneous clustering (clusters whose nodes are degree-equivalent). In this paper, we extend this model to investigate networks that contain clusters whose nodes are not degree-equivalent, including multilayer networks. Through numerical examples we show how this method can be used to investigate the properties of random complex networks with arbitrary clustering, extending the applicability of the configuration model and generating function formulation.
