Gleeson James P, Melnik Sergey
Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 2):046121. doi: 10.1103/PhysRevE.80.046121. Epub 2009 Oct 26.
An analytical approach to calculating bond percolation thresholds, sizes of k-cores, and sizes of giant connected components on structured random networks with nonzero clustering is presented. The networks are generated using a generalization of Trapman's [P. Trapman, Theor. Popul. Biol. 71, 160 (2007)] model of cliques embedded in treelike random graphs. The resulting networks have arbitrary degree distributions and tunable degree-dependent clustering. The effect of clustering on the bond percolation thresholds for networks of this type is examined and contrasted with some recent results in the literature. For very high levels of clustering the percolation threshold in these generalized Trapman networks is increased above the value it takes in a randomly wired (unclustered) network of the same degree distribution. In assortative scale-free networks, where the variance of the degree distribution is infinite, this clustering effect can lead to a nonzero percolation (epidemic) threshold.
提出了一种分析方法，用于计算具有非零聚类的结构化随机网络上的键渗流阈值、k核大小和巨型连通分量的大小。这些网络是使用Trapman [P. Trapman, Theor. Popul. Biol. 71, 160 (2007)] 的嵌入树状随机图中的团模型的推广生成的。生成的网络具有任意的度分布和可调的度相关聚类。研究了聚类对这类网络键渗流阈值的影响，并与文献中的一些最新结果进行了对比。对于非常高的聚类水平，这些广义Trapman网络中的渗流阈值会增加到高于具有相同度分布的随机布线（无聚类）网络中的值。在度分布方差为无穷大的 assortative 无标度网络中，这种聚类效应可能导致非零的渗流（流行）阈值。
