论文标题
具有高阶聚类的随机渗透
Percolation in random graphs with higher-order clustering
论文作者
论文摘要
渗透理论可用于使用生成函数公式来描述复杂网络的结构特性。该映射假设网络是局部树状的，并且不包含邻居之间的短距离环路。在本文中，我们使用生成功能公式来检查包含任何顺序的简单周期和集团的聚类网络。我们使用对这些网络的Molloy reed标准的自然概括来描述它们的关键属性，并得出对巨型组件大小的分析描述，从而为泊松和幂律网络提供了解决方案。我们发现，包括较大简单周期的网络行为越来越类似树。群集由较大的集团组成的群集越来越偏离树状溶液，尽管该行为很大程度上取决于程度分层。
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.
