复杂网络中节点重要性Damage度量分析

Analysis on Damage Measure of Vertex Importance in Complex Networks

为从网络健壮性角度研究复杂网络中节点重要性指标Damage问题,理论分析了各类模拟网络包括Barabasi-Albert无标度网络、Erdos-Renyi随机网络以及树形网络上的Damage度量。实证分析了真实网络上Damage指标对于网络功能的影响以及Damage与度的相关性。通过统计分析比较了真实网络在面对Damage攻击及度攻击时的抵御能力。理论与实证分析结果表明:各类复杂网络中存在着数量不可忽视的Damage较大的节点;Damage是一种不可代替的衡量网络节点重要性的指标;Damage较大的节点对于真实网络的功能有重要影响。对于各种不同的网络,对比度攻击和Damage攻击过程,发现存在1个交叉点,在此点之前Damage攻击比度攻击更具破坏性。

To research the vertex importance index--Damage in complex networks from the perspective of robustness of complex networks, the Damage measures of vertices in synthetic networks including Barabasi-Albert, Erdos-Renyi, tree-like networks and real complex networks are theoretically analyzed. The influences of Damage on network functions and the correlations between Damage and degrees are empirically analyzed. The resisting abilities of real networks against Damage attacks and degree attacks are compared by statistical analyses. The theoretical and empirical analyses show that：there exist many non-ignorable vertices with large Damage in complex networks; Damage is one of the non-replaceable indexes measuring the importance of vertices;vertices with large Damage value are important for maintaining the functionality of networks. For a variety of networks, the results from comparison of the degree attack with the Damage attack processes show the Damage attack before a crossover point is more destructive than the degree attack.