无标度网络的嵌入-删除-补偿模型的建立及分析

Analysis of Scale-free Networks Based on the Insertion-deletion-compensation Model

Barabási-Albert(B-A)模型是一种生长网络模型,其动力学特征是新节点的嵌入和链接的偏好选择.基于B-A模型,本文把模型的动力学过程推广到包括对网络中已有节点(或链接)的随机删除及其相应链接补偿.研究表明网络的无标度特征(幂律指数γ=3)本质上是因为链接的偏好特性,而与随机增加或删除节点或链接无明显关系.本研究结果能够从网络动力学方面解释无标度网络(scale-freenetworks)对随机攻击具有鲁棒性和对恶意攻击具有脆弱性的原因.

From the Barabási-Albert (BA) construction based on growth and preferential attachment, this paper introduces a model, in which, the dynamics are introduced by the insertion of a new node, the random deletion of the existing links and the compensation for the lost links. The result shows that whatever insertion and deletion rates are, true scale-free structures would emerge, where the degree distributions obey a power law with an exponent of 3. It is the preferential attachment that essentially governs the scale-free structures. The dynamics reported in this paper can be applied to the reasons why the scale-free networks possess the robust-yet-fragile property, that is, they are robust against random failures of nodes but fragile to intentional attacks.