The structure of many real networks is not locally treelike and, hence, network analysis fails to characterize their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, arXiv:2006.06744], 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.

中文翻译：

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具有任意聚类的随机图及其应用

许多实际网络的结构不是本地树状的，因此，网络分析无法描述其键渗透特性。在最近的一篇论文中[P. [Mann，VA Smith，JBO Mitchell和S. Dobson，arXiv：2006.06744]，我们针对具有均质聚类（节点的度数相等的簇）的随机网络的渗流特性开发了解析解决方案。在本文中，我们扩展了该模型以研究包含节点不等于度的群集的网络，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，扩展配置模型的适用性并生成函数公式。