Complexity of networks: A structural heterogeneity approach

The complexity measurement of networks is one of the hot topics in complex networks. How to accurately describe the complexity difference between networks is helpful to the study of network structure. This paper proposes a method for measuring the network complexity considering the local and global structural heterogeneity. This method introduces the k-order neighbors to examine the local structural heterogeneity. Besides, the standard deviation is used to evaluate the global structural heterogeneity. Based on this, the complexity measurement model is established. In order to testify the efficiency of the method, the ER random networks, BA scale-free networks and real networks (including four social networks and two infrastructure networks) are used for experiments. The results show that the proposed method is sensitive and can effectively describe the subtle difference of structure complexity between networks.