小世界网络抗毁性及介-度相关性研究

日常生活中,复杂网络主要面临随机攻击和选择性攻击,网络模型的结构特性使复杂网络在不同攻击方式下的抗毁性有很大的差异.综合考虑复杂网络的抗毁性参数和网络模型的结构特性差异,文章以节点的最大度值、平均度值、最大介数和平均介数为度量参数,通过5种不同攻击方式对WS小世界网络的抗毁性进行了测试,得到了介度关系曲线,随着节点的移除,动态分析了WS小世界网络的抗毁性和攻击下小世界网络的介 度相关性.实验结果表明,WS小世界网络在RD攻击下表现出一定的脆弱性,在其他攻击方式下有很强的鲁棒性,而其介度关系在某些区域呈线性关系,但大部分区域呈现无规律性,其动态相关性需要进一步研究.小世界网络较强的抗毁性对组建网络有重要的影响,鉴于小世界网络的结构特性,组建网络时应尽量不要把网络的功能集中在少数Hub节点上.针对WS小世界网络较强的鲁棒性,结合小世界网络的结构特性,将做进一步研究,以便提出更高效的攻击策略.

A Study of Invulnerability of Small World Network and the Correlation of Betweenness-Degree

In daily life, complex networks mainly undergo two types of damages： random failure and selective attack. The structural features of various network models make the capability of complex networks that resist attacks very different. Considering the invulnerability parameters and structural properties of complex networks, we have a comprehensive evaluation on of a small-world network by measuring node average degree, max degree, average betweenness centrality and max betweenness centrality under various attacks. With the removing of nodes, we estimate the invulnerability of the network by analyzing the relationship of node degree and betweenness centrality. The experimental results show that small-world network is more vulnerable under RD, while has strong robustness under other attack strategies. The experimental results show that the relationship between node degree and betweenness centrality of a small-world network is linear in some range, while it is irregular in most regions. The strong robustness of WS small-world networks has an important influence on building real networks. According to the structural features of small-world networks, we should not put the fimction of networks on a few Hub nodes. To improve more efficient strategies, we will make a further research.