基于强度信息维数的加权网络分形特性分析

Fractal Characteristics Analysis of Weighted Networks Based on Strength Information Dimension

信息维数是从信息量的角度揭示复杂网络分形特性。现有的加权网络信息维数法仅仅用到了加权网络盒子覆盖法中的盒子尺寸选择规则,本文进一步考虑盒子中节点间的边权信息,重新将盒子包含信息的概率定义为盒子中所有节点的强度和与网络中所有节点的强度和的比值,提出了一种分析加权网络分形特性的强度信息维数法。该算法运用在谢尔宾斯基(Sierpinski)和康托三角尘(Cantor Dust)两类构造加权网络中,计算所得的强度信息维数与网络的理论维数非常接近,并在3个真实加权网络与现有加权网络信息维数法以及加权网络盒子覆盖法进行比较,实验结果表明3个算法都度量加权网络的分形特性,但是从拟合效果和拟合误差来看本文算法略优。

Information dimension reveals the fractal characteristics of complex networks from the perspective of information content.The existing information dimension algorithm of weighted network only uses the box size selection rules of the box coverage algorithm of weighted network.This paper further considers the information of edge weight between nodes in the box,and redefines the probability of the box containing information as the ratio of the sum of the strength of all nodes in the box to the sum of the strength of all nodes in the network.A strength information dimension algorithm is proposed to analyze the fractal characteristics of weighted networks.This algorithm is applied to two kinds of constructed weighted networks,Sierpinski and Cantor Dust,and the strength information dimension calculated is very close to the theoretical dimension of the network,and the algorithm is compared with the existing information dimension algorithm and box covering algorithm of weighted network in three real weighted networks.The experimental results show that the three algorithms all measure the fractal characteristics of the weighted network,but the algorithm in this paper is slightly better in terms of fitting effect and fitting error.