Construction and Applications of Null Models for Unweighted Networks

The static unweighted network, whose null models have been studied widely and thoroughly, is the most common type of complex networks at present. In this study, we classify an unweighted network into two types of networks: undirected network and directed network. We study the construction and applications of null models for the two kinds of networks, especially the null models of unweighted undirected network are emphasized. Firstly, we illustrate the definitions of null models from low to high orders for unweighted undirected network according to the theory of random graph series. And then we describe the constructing process and related applications for 1 k-3 k null models by using ER random graph, configuration model, edge swapping, and so on. For the edge swapping algorithm, which is the most important mode for constructing null models, we introduce non-tendentious random edge swapping, tendentious assortative or dis-assortative edge swapping, and local edge swapping for detecting whether the rich-club properties exist in a network. Moreover, the high order null models are firstly extended to analyze meso-scale network features such as community detection. Finally, we analyze 1 k null models of directed network and tried to detect four types of in-out degree assortativities. In this study, we find that null models can not only provide an accurate baseline for real-life networks, but also qualitatively and quantitatively describe non-trivial properties of empirical complex networks. © 2019, Editorial Board of Journal of the University of Electronic Science and Technology of China. All right reserved.