一类高聚类系数的加权无标度网络及其同步能力分析

针对真实世界中大规模网络都具有明显聚类效应的特点, 提出一类具有高聚类系数的加权无标度网络演化模型, 该模型同时考虑了优先连接、三角结构、随机连接和社团结构等四种演化机制. 在模型演化规则中, 以概率p增加单个节点, 以概率1–p增加一个社团. 与以往研究的不同在于新边的建立, 以概率φ在旧节点之间进行三角连接, 以概率1–φ进行随机连接. 仿真分析表明, 所提出的网络度、强度和权值分布都是服从幂律分布的形式, 且具有高聚类系数的特性, 聚类系数的提高与社团结构和随机连接机制有直接的关系. 最后通过数值仿真分析了网络演化机制对同步动态特性的影响, 数值仿真结果表明, 网络的平均聚类系数越小, 网络的同步能力越强. 关键词： 无标度网络 加权网络 聚类系数 同步能力

A weighted scale-free network model with high clustering and its synchronizability

The detecting of clusters or communities in large real-world networks such as large social or information networks is of considerable significance. We propose a new weighted evolving model of high clustering scale-free network incorporating a community structure mechanism, which means the addition of the new node depends on not only a single node but also a community. In the process of the evolution, a new node with probability p and a new community with the probability 1–p are added to the network. Different from the existing studies where new links are additionally established, some links with probability φ according to the triad formation mechanism and other links with the probability 1–φ according to the random selection mechanism are connected between neighbors in the model. The topology and weights of links of the network evolve as time goes on. Moreover, the evolving model gives power-law distributions of degree, weight, and strength as confirmed in several real world systems. Especially, the average clustering coefficient exhibits power-law decay as a function of degree of node. Both the community structure and the triad formation can enhance the average clustering coefficient of scale-free networks. Furthermore, we investigate how the synchronization of the network is influenced by the evolution mechanism of the network. Numerical simulation results show that the network synchronizability is optimized when the average clustering coefficient decreases in the model.
Keywords： scale-free network weighted network clustering coefficient synchronizability