Exact Signed Modularity Density Maximization Solutions and Their Real Meaning

In the context of social media analyses, signed social networks are important representations of relationships between entities. These networks can represent positive or negative relationships between every two entities of a social network. One of the usual analyses over social networks is the communities/clustering search. In this paper, we report analyses on the Signed Modularity Density Maximization problem, which searches for meaningful clusters inside a signed social network. In this analysis, we present a new branch-and-price algorithm to find optimal solutions to this problem. The optimal solutions of two real signed networks and some artificial networks are generated and analyzed. The results suggest that the problem finds meaningful clusterings in signed social networks, and some parameters are suggested to obtain the best results.