具有高阶聚类的随机图的渗流
Percolation in random graphs with higher-order clustering
摘要：
逾渗理论可以用生成函数来描述复杂网络的结构特性。这种映射假设网络是局部树状的，并且不包含邻居之间的短程环路。在本文中，我们使用的生成函数制定检查集群网络，包含简单的周期和集团的任何顺序。我们使用自然概括的Molloy-Reed标准，这些网络来描述他们的临界特性，并推导出一个分析描述的巨型组件的大小，提供解决方案的泊松和幂律网络。我们发现，网络包括较大的简单循环的行为越来越像树。Conversley，由较大的集团组成的聚类越来越偏离树状解决方案，尽管行为强烈依赖于度的可伸缩性。
英文摘要：
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 tree-like and does not contain short-range loops between neighbours. 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 generalisation to the Molloy-Reed criterion for these networks to describe their critical properties and derive an 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 tree-like. Conversley, clustering comprised of larger cliques increasingly deviate from the tree-like solution, although the behaviour is strongly dependent on the degree-assortativity.
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