多社团加权复杂网络建模及其级联抗毁性研究

Research on Modeling and Cascading Invulnerability of Weighted Complex Networks with Community Structure

为了研究社团结构和权重因素对网络级联抗毁性的影响,引入节点和边的消亡机制,建立了一类具有社团结构的加权网络模型.采用本方法生成网络的度、强度和边权分布都呈现无标度特性,比现有BBV(Barrat-Barthelemy-Vespignani)模型具有更好的社团结构特性,且幂律指数、模块度参数可调.在此基础上研究了网络的级联抗毁性,采用节点及其邻居节点强度的函数定义网络负荷,故障节点负荷采用"局部定义,局部分配"的策略.仿真分析了边权演化参数、模块度函数、攻击策略和演化时间对网络级联抗毁性的影响.结论表明,网络的抗毁性与边权演化参数、网络演化时间成反比,与模块度的关系不是单调的而是存在一个阈值.优先攻击度最大节点的策略对网络抗毁性破坏最大,且在多节点遭受攻击时,网络的故障规模会发生突变.文章的研究结论对故障的预防与控制以及网络的建设具有一定的参考价值.

In order to study the influence of community structure and weight factors on cascade invulnerability of networks,a weighted network model with community structure is established by introducing the extinction mechanism of nodes and edges.The degree,intensity and edge weight distribution of the network generated by this method are scale-free,and have better community structure characteristics than the existing BBV(Barrat-Barthelemy-Vespignani)model,and the power law index and modularity parameters can be adjusted.On this basis,cascade invulnerability of the network is studied.The network load is defined by the function of the strength of nodes and their neighbors,and the fault node load is defined by the strategy of"local definition,local distribution".The influence of edge weight evolution parameters,modularity function attack strategy and evolution time on network cascade invulnerability is simulated and analyzed.The conclusion shows that the invulnerability of the network is inversely proportional to the evolution parameters of edge weights and the evolution time of the network.The relationship between the invulnerability and the modularity is not monotonous,but there is a threshold.The strategy of the node with the highest degree of priority attack destroys the network’s invulnerability most,and the scale of network failure will change abruptly when multiple nodes are attacked.The conclusion of this paper has a certain reference value for the prevention and control of faults and the construction of network.