Disassortativity of percolating clusters in random networks
Disassortativity of percolating clusters in random networks
复制标题
DOI：
10.1103/physreve.98.062314
复制
发表时间：
2018-07
影响因子：
2.4
通讯作者：
S. Mizutaka;T. Hasegawa
中科院分区：
文献类型：
--
作者：
S. Mizutaka;T. Hasegawa
本文讨论了不相关随机网络上的逾渗过程所形成的巨组分的度-度相关性。使用生成函数，我们推导出一个一般表达式的巨组件，$r$，这是定义为皮尔逊的相关系数直接连接节点的程度的相关性。对于度分布的三阶矩有限的不相关随机网络，我们证明了以下两点。(1)对于p\ge p_{\rm c}，配位性r满足关系r\le 0。(2)在逾渗阈值处，度为-k$的节点的相邻节点的平均度与k^{-1}$成正比，与度分布函数无关。这些结果表明，在渗流阈值附近的巨组分中出现了扩散性。分析处理的准确性证实了广泛的Monte Carlo模拟。
We provide arguments for the property of the degree-degree correlations of giant components formed by the percolation process on uncorrelated random networks. Using the generating functions, we derive a general expression for the assortativity of a giant component, $r$, which is defined as Pearson's correlation coefficient for degrees of directly connected nodes. For uncorrelated random networks in which the third moment for the degree distribution is finite, we prove the following two points. (1) Assortativity $r$ satisfies the relation $r\le 0$ for $p\ge p_{\rm c}$. (2) The average degree of nodes adjacent to degree-$k$ nodes at the percolation threshold is proportional to $k^{-1}$ independently of the degree distribution function. These results claim that disassortativity emerges in giant components near the percolation threshold. The accuracy of the analytical treatment is confirmed by extensive Monte Carlo simulations.