AI 中文总结
研究经历有限次键渗流的随机网络结构，定义竞争与协作分支过程，用生成函数法研究其行为，包括GCC预期大小等，还针对特定随机图探索该模型，此模型可作疾病传播的季节性N菌株模型。
AI 中文摘要
在本文中，我们研究了经历任意但有限次数键渗流的随机网络的涌现结构。我们定义了两种类型的顺序分支过程：一种竞争分支过程，其中每次迭代对前几代产生的剩余图（RG）执行键渗流；另一种协作分支过程，其中渗流是在巨型连通分量（GCC）上进行的。我们使用生成函数的解析精确方法研究这些模型的行为，包括给定代的 GCC 的预期大小、临界渗流概率以及所得图结构的其他拓扑属性。我们针对厄多斯 - 雷尼和无标度随机图探索了该模型。该模型可解释为疾病传播的季节性 N 菌株模型。
英文摘要
In this paper we examine the emergent structures of random networks that have undergone bond percolation an arbitrary, but finite, number of times. We define two types of sequential branching processes: a competitive branching process - in which each iteration performs bond percolation on the residual graph (RG) resulting from previous generations; and, a collaborative branching process - where percolation is performed on the giant connected component (GCC) instead. We investigate the behaviour of these models, including the expected size of the GCC for a given generation, the critical percolation probability and other topological properties of the resulting graph structures using the analytically exact method of generating functions. We explore this model for Erdos-Renyi and scale free random graphs. This model can be interpreted as a seasonal N-strain model of disease spreading.
Comments23 pages, 13 figures
Journal refPhys. Rev. E 106, 014304 - Published 20 July, 2022
DOI：10.1103/PhysRevE.106.014304
