随机派系生长网络模型及其传输能力研究

Random clique evolving network model and their communicability

本文提出一种基于随机选择的派系生长网络模型,该网络从一个a-派系模体开始,每个时间步t,在网络中随机选择m个节点构建一个新的a-派系,由此网络生长演化.模拟研究表明:该网络具有高的聚类系数和短的平均路径长度是一个小世界网络,并且比值ρ=m/a越小,聚类系数越大.而度分布则呈指数分布,这些特征与许多交通系统的复杂网络的实证研究结果相符.该网络的聚类系数与节点度呈幂律变化,显示网络具有模块化层次结构的特征,这一特征与近年来人们研究的大多数复杂网络具有模块化层次结构特征的实证研究结果相符.我们还研究了该网络的传输能力,研究表明该网络的传输能力随着比值ρ=m/a的减小而增大.这些研究结果对城市公共交通网络的构建具有一定的指导意义.

We introduce a notion of random clique evolving network, this network start from a complete subgraph of a-clique, where a is the size of the clique. In every time step T, m nodes are chosen from this network randomly, and forming a new complete subgraph of a-clique. In this way, this network grows in time steps. The numerical investigation shows that the cumulative degree distribution of this network takes an exponential function, which is the property of the homogeneous networks, and the clustering coefficient of this network is larger than that of the ER network. However, the characteristic path length of this network is the similar to that of the ER network, so this network shows the behaviors of small-world networks. Subsequent study shows that this network exhibits hierarchical modular structure for the clustering spectrum vs. k takes power-law. These results are in good agreement with the empirical results on many real-world complex networks, such as urban bus translation network or urban subway network, our model can explain the evolutionary procedure of these spatial networks. What＇s more, we present a numerical investigation on the communicability of our model by the Estrada index EE（G）, the Estrada index EE（G） of this network increases with decreasing the rata m/a at the same size N and the same average degree 〈k〉, The communicability of the urban public translation networks is very important, our results have urban bus translation network and urban subway network. a certain guiding significance for the construction of