Constructing refined null models for statistical analysis of signed networks* *Project supported by the National Natural Science Foundation of China (Grant Nos. 61773091 and 61603073), the LiaoNing Revitalization Talents Program (Grant No. XLYC1807106), and the Natural Science Foundation of Liaoning Province, China (Grant No. 2020-MZLH-22).

Abstract

The establishment of effective null models can provide reference networks to accurately describe statistical properties of real-life signed networks. At present, two classical null models of signed networks (i.e., sign and full-edge randomized models) shuffle both positive and negative topologies at the same time, so it is difficult to distinguish the effect on network topology of positive edges, negative edges, and the correlation between them. In this study, we construct three refined edge-randomized null models by only randomizing link relationships without changing positive and negative degree distributions. The results of nontrivial statistical indicators of signed networks, such as average degree connectivity and clustering coefficient, show that the position of positive edges has a stronger effect on positive-edge topology, while the signs of negative edges have a greater influence on negative-edge topology. For some specific statistics (e.g., embeddedness), the results indicate that the proposed null models can more accurately describe real-life networks compared with the two existing ones, which can be selected to facilitate a better understanding of complex structures, functions, and dynamical behaviors on signed networks.