Community detection in signed networks: A penalized semidefinite programming framework

Network theory provides a powerful framework for modeling complex systems by representing relationships between entities. While traditional networks encode the presence or absence of interactions, many real-world systems, such as social networks and biological systems, require distinguishing between positive (cooperative) and negative (antagonistic) relationships to capture their underlying dynamics. Signed networks address this need by incorporating edge signs, enabling a more nuanced representation of system structures. In this paper, we study community detection in signed networks under the signed stochastic block model (SSBM). We propose a novel penalty-enhanced semidefinite programming approach, which is derived from a relaxation of maximum likelihood estimation under assumptions of network sparsity. This method explicitly models the asymmetry between positive and negative edges. Our framework is theoretically proven to achieve accurate community recovery, and its practical effectiveness is demonstrated through experiments on both synthetic and real-world datasets.