Nie S（聂森）, Wang XW（王旭文）, Zhang HF（张海峰）,

Li QL,（李启朗），Wang BH（汪秉宏）

Robustness of Controllability for

Networks Based on Edge-Attack. 

PLoS ONE (2014) 9(2): e89066. doi:10.1371/

 journal.pone.0089066

Abstract

We study the controllability of networks in the process of cascading failures under two different attacking strategies, random and intentional attack, respectively. For the highest-load edge attack, it is found that the controllability of Erdo˝s-Re´nyi network, that with moderate average degree, is less robust, whereas the Scale-free network with moderate power-law exponent shows strong robustness of controllability under the same attack strategy. The vulnerability of controllability under random and intentional attacks behave differently with the increasing of removal fraction, especially, we find that the robustness of control has important role in cascades for large removal fraction. The simulation results show that for Scale-free networks with various power-law exponents, the network has larger scale of cascades do not mean that there will be more increments of driver nodes. Meanwhile, the number of driver nodes in cascading failures is also related to the edges amount in strongly connected components.

边受攻击网络之可控性坚固程度

本文研究了在不同的边攻击策略下，网络的可控性能在级联失效中的变化情况。首先研究了删除负载最大边的情况，其中负载为边介数：研究表明，ER网络的可控性能在平均度适中的情况下鲁棒性较差，而SF网络的可控性能在幂律指数适中的情况下鲁棒性较好，同时，对于平均度较小的SF网络，不同的幂律指数使得网络的失效边数不一样，但是失效前后所需的驱动节点数目增量却相差不大。另外，我们研究了按比例删除边数的情况，分为随机删除和蓄意删除两种策略，其中蓄意删除指按照边的负载大小排列，从大到小成一定比例删除。研究发现，在不同的删除方式下，网络可控性能随着删除边数的增加呈现交替变化并与网络结构相关，当删除边数比例适中时，蓄意删除容易抑制级联失效的传播，影响可控性的变化。当删除边数比例较大时，级联失效停止，此时网络的可控性能与删除的边的不同结构类型相关（critical, ordinary, redundant）。最后，利用实证数据验证了我们的仿真结论。出于计算的考虑，本文中可控性能的计算是基于最大匹配方法的结构可控性，而对于此与精确可控之间的差别，在补充材料中我们也做了进一步的对比，结果表明：对于较大规模的ER和SF网络在给定边权的情况下，两种计算方法结果一致；对于实证网络，给定边权时，精确可控计算的驱动节点数值比结构可控计算的结果大，而随机边权时，两者结果一致。

PLoS ONE (2014) 9(2) 全文下载：

journal.pone.0089066 聂森.pdf