The Family of Assortativity Coefficients in Signed Social Networks

Signed networks are a special type of networks with both positive and negative edges, and the signs of links play a significant role in functional analysis and structural evolution. Because of the particularity of signed networks, the existing methods to measure their degree assortativity only rely on dividing the original network by link signs ignoring the signs of node degrees, which cannot measure the complicated degree mixing patterns. In this study, considering the complex types of link signs and node degree signs, we propose four new mixing patterns that have not been measured before for signed social networks and define a set of six signed assortativity measures based on traditional assortativity coefficients, to form a complete family of assortativity coefficients. The statistical significance of the family of assortativity coefficients is confirmed by comparing with null models, showing the assortativity significance profile (ASP) of different empirical signed networks. Besides, the relationship and distinction between the family of assortativity coefficients and classical network indexes, such as excess average degree and network embeddedness, are analyzed, revealing the endogenous complexity of signed social networks and the diversity of their assortativities. The proposed method enriches the assortativity diversity of social networks, which is beneficial to measure and analyze complex structure, function, and evolution of real-world social networks.