Characterizing the structural complexity of networks is a major challenging work in network science. However, a valid measure to quantify network complexity remains unexplored. Although the entropy of various network descriptors and algorithmic complexity have been selected in the previous studies to do it, most of these methods only contain local information of the network, so they cannot accurately reflect the global structural complexity of the network. In this paper, we propose a statistical measure to characterize network complexity from a global perspective, which is composed of the communicability sequence entropy of the network and the associated Jensen-Shannon divergence. We study the influences of the topology of the synthetic networks on the complexity measure. The results show that networks with strong heterogeneity, strong degree-degree correlation, and a certain number of communities have a relatively large complexity. Moreover, by studying some real networks and their corresponding randomized network models, we find that the complexity measure is a monotone increasing function of the order of the randomized network, and the ones of real networks are larger complexity-values compared to all corresponding randomized networks. These results indicate that the complexity measure is sensitive to the changes of the basic topology of the network and increases with the increase of the external constraints of the network, which further proves that the complexity measure presented in this paper can effectively represent the topological complexity of the network.

• Received 20 June 2019
• Accepted 31 March 2020

DOI:https://doi.org/10.1103/PhysRevE.101.042305