Verification and prediction of structural balance: A data-driven perspective

The structural balance plays a fundamental role in networked systems with both attractive and repulsive interactions, which can be characterized by a signed network. In this paper, we show that the ensemble of type of interaction in a signed network can be inferred from the eigenvector of the signed Laplacian matrix. Also, it has been shown that a graph, derived from the graph Cartesian product of factor graphs, is structurally balanced if and only if its factors are structurally balanced. According to the theoretical results, the verification and prediction of the structural balance of the signed network is presented from a data-driven perspective by utilizing the dynamic mode decomposition.