网络收缩过程中Erd {\H o} s-Rényi图结构的收敛性
Convergence towards an Erd{\H o}s-Rényi graph structure in network contraction processes
摘要：
20年前，巴拉巴西（Barabási）和阿尔伯特（Albert）在一篇极具影响力的论文中[Science 286，509（1999）]指出，经历偏好连接的一般增长过程的网络会向无标度结构演化。在任何有限的系统中，增长最终都会停滞，并且可能会由于节点故障，攻击或流行病而导致网络收缩。使用主方程制定和计算机模拟，我们分析了网络的结构演化收缩过程通过随机，优惠和传播节点删除。我们发现，收缩网络收敛到一个Erd {\H o} s-Rényi网络结构，其平均度继续减少的收缩进行。这表现为度分布向泊松分布的收敛和度-度相关性的丧失。
英文摘要：
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.
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