复杂网络信息维数的推广

Generalization of the Information Dimension of Complex Networks

信息维数是从信息量的角度来度量复杂网络分形特性的常用指标。在现有的基于盒子覆盖法的复杂网络信息维数概念上,进一步考虑网络节点间的差异性,将每个盒子包含信息的概率定义为该盒子内节点度的总和与网络中所有节点度的总和之间的比值,提出了一种新的复杂网络信息维数计算方法。在5个真实网络数据集上进行分形分析,并将分析结果与利用基于盒子覆盖法的复杂网络信息维数法得到的结果以及利用盒维数法得到的结果进行对比。研究结果表明:新的信息维数法计算所得的信息维数值与网络的盒维数值相近,并且该方法同样能够较好的度量实际网络的分形特性。

The information dimension is a common quality to measure the fractal property of complex networks from the perspective of information content.Based on the existed definition of information dimension of complex networks,we consider further the difference between network nodes,and define firstly the probability of information containing the box as the ratio of the sum of nodes degree in that box to the sum of nodes degree in the network.Then we propose a new information dimension of complex networks according to the probability of information containing the box.The proposed method was applied to calculate the fractal dimensions of five real-world complex networks.The simulation results show that the fractal dimensions obtained by the proposed method are very close to the existed information dimension method and the classical box-covering method,which demonstrate that the proposed method can dealing with the fractal dimension problem of complex networks effectively.