Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally treelike and does not contain short-range loops between neighbors. In this paper we use the generating function formulation to examine clustered networks that contain simple cycles and cliques of any order. We use the natural generalization to the Molloy-Reed criterion for these networks to describe their critical properties and derive an approximate analytical description of the size of the giant component, providing solutions for Poisson and power-law networks. We find that networks comprising larger simple cycles behave increasingly more treelike. Conversely, clustering composed of larger cliques increasingly deviate from the treelike solution, although the behavior is strongly dependent on the degree-assortativity.

中文翻译：

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具有高阶聚类的随机图中的渗流

渗流理论可用于使用生成函数公式描述复杂网络的结构特性。该映射假定网络在本地是树状的，并且在邻居之间不包含短距离环路。在本文中，我们使用生成函数公式来检查包含简单循环和任意阶团的聚类网络。我们使用自然泛化到这些网络的Molloy-Reed准则来描述它们的关键特性，并得出巨型组件大小的近似分析描述，从而为Poisson和幂律网络提供解决方案。我们发现，包含较大简单循环的网络的行为越来越像树。相反，由较大集团组成的聚类越来越偏离树状解决方案，