权重分布对加权网络效率的影响

Effect of distribution of weight on the efficiency of weighted networks

加权网络可以对复杂系统的相互作用结构提供更加细致的刻画,而改变边权也成为调整和改善网络性质与功能的新途径.基于已有无权网络的效率概念,文中给出了相似权和相异权网络的网络效率定义,并研究了权重分布对于网络效率的影响.从平权的规则网络出发,通过改变权重的分布形式考察权重分布对网络效率的影响,结果发现,在规则网络上,权重分布随机性的增加提高了网络效率,而在几种常见的权重分布形式中,指数分布对网络效率的改进最为显著.同时,权重随机化之后网络最小生成树的总权重减小,意味着网络的运输成本随着权重异质性的增加而降低.以上结果为深入理解权重对网络结构与功能的影响提供了基础.

Weighted networks can give more detailed description of interaction between agents of corresponding systems. Link weight also provides another way to improve the properties and functions of networks. Based on the concept of network efficiency in binary networks,in this paper,the efficiency of weighted networks with similarity or dissimilarity weight is defined. The effect of weight distribution on the network efficiency are investigated. From the initial regular network with homogeneous link weights,a method is introduced to randomize the weight distribution over the links. The results demonstrate that the random redistribution of link weight can improve the network efficiency. Moreover,exponential distribution of link weight shows more significant improvement compared with the other common distributions,such as uniform,Poisson, Gauss, and power law distributions. Meanwhile, it is also found that the total weight of the corresponding minimum spanning tree is reduced with the randomization of link weight. That means the cost of transportation is decreased with the increase of link weight heterogeneity. All these results can help us get deeper understanding about the effect of link weight on the property and function of networks.