论文标题
网络收缩过程中的ERD {\ h o} s-rényi图结构的收敛
Convergence towards an Erd{\H o}s-Rényi graph structure in network contraction processes
论文作者
论文摘要
在二十年前的一份极富影响力的论文中，巴拉巴西和阿尔伯特[科学286，509（1999）]表明，正在接受通用增长过程的网络，并优先地依赖于无尺度的结构。在任何有限的系统中，增长最终都会失速，并且由于节点故障，攻击或流行病而可能是网络收缩阶段。使用主方程公式和计算机模拟，我们通过随机，优先和传播节点删除来分析受收缩过程受到收缩过程的结构演变。我们表明，合同网络趋于ERD {\ h o} s-rényi网络结构，其平均度随着收缩的进行而继续降低。这是由程度分布向泊松分布的收敛性和程度相关性损失所表明的。
In a highly influential paper twenty years ago, Barabási and Albert [Science 286, 509 (1999)] showed that networks undergoing generic growth processes with preferential attachment evolve towards scale-free structures. In any finite system, the growth eventually stalls and is likely to be followed by a phase of network contraction due to node failures, attacks or epidemics. Using the master equation formulation and computer simulations we analyze the structural evolution of networks subjected to contraction processes via random, preferential and propagating node deletions. We show that the contracting networks converge towards an Erd{\H o}s-Rényi network structure whose mean degree continues to decrease as the contraction proceeds. This is manifested by the convergence of the degree distribution towards a Poisson distribution and the loss of degree-degree correlations.
