不同权重定义下的静态与动态加权网络的比较分析

Comparison of Static and Dynamic Weighted Networks with Various Weight Definitions

形成加权网络的方法有2类:静态和动态方法,以往的研究中并没有对2种方法进行比较分析。采用3种权重定义的方法,即分配常数的边权重、服从指数分布的边权重、节点度乘积函数的边权重,分析了2种形成方法下加权网络强度分布的不同特性。研究表明,对于静态方法形成的加权网络,其强度分布对于不同权重定义有较大差别;对于动态方法形成的加权网络,其度分布与初始权重的定义没有必然联系,只要在演化过程中满足"强度择优性",就可得到幂律分布。虽然用静态方法形成的加权网络易于分析,但由于动态方法形成的加权网络的度分布有不依赖于权重定义的特性,所以用动态方法的形成加权网络比较优越。

Aim. There are two main methods for constructing weighted networks ： static and dynamic. As, to our knowledge, there does not exist any paper in the open literature on the comparison of these two main methods, we now present such a paper. In the full paper, we explain our method of comparison and simulation results in some detail. In this abstract, we just add some pertinent remarks to listing the two topics of explanation. The first topic is.. basic concepts. In the first topic, we introduce three weight definitions： constant link weight, link weight obeying the exponential distribution, and link weight equal to the product of the degrees of two end points of the link. Also in the first topic, we point out after some discussion that the ideal degree distribution of a weighted network is the one that obeys the power-law distribution. The second topic is. the comparison of static weighted network with dynamic weighted network. The subtopics of the second topic are： static weighted network （subtopic 2. 1）, dynamic weighted network （subtopic 2. 2）, and simulation results and their analyses （subtopic 2.3）. Although there are details in subtopics 2.1 and 2. 2 worth mentioning, they are omitted in this abstract. Even in subtopic 9.. 3, we limit ourselves to just mentioning the most important things. The simulation results are given in nine figures in the full paper. The main result of analyses is that, for the dynamic method, as long as in the evolving process the preferential strength mechanism is adopted, the degree distribution of the weighted network always obeys the power-law distribution and it is independent of the original weight definitions; therefore, the weighted network formed by the dynamic method is superior to that formed by the static method.