Visualizing Structural Balance in Signed Networks

Abstract

Network visualization has established as a key complement to network analysis since the large variety of existing network layouts are able to graphically highlight different properties of networks. However, signed networks, i.e., networks whose edges are labeled as friendly (positive) or antagonistic (negative), are target of few of such layouts and none, to our knowledge, is able to show structural balance, i.e., the tendency of cycles towards including an even number of negative edges, which is a well-known theory for studying friction and polarization. In this work we present Structural-balance-viz: a novel visualization method showing whether a connected signed network is balanced or not and, in the latter case, how close the network is to be balanced. Structuralbalance-viz exploits spectral computations of the signed Laplacian matrix to place network's nodes in a Cartesian coordinate system resembling a balance (a scale). Moreover, it uses edge coloring and bundling to distinguish positive and negative interactions. The proposed visualization method has characteristics desirable in a variety of network analysis tasks: Structural-balance-viz is able to provide indications of balance/polarization of the whole network and of each node, to identify two factions of nodes on the basis of their polarization, and to show their cumulative characteristics. Moreover, the layout is reproducible and easy to compare. Structural-balance-viz is validated over synthetic-generated networks and applied to a real-world dataset about political debates confirming that it is able to provide meaningful interpretations.

World War III analysis using signed social networks

“…It is worth noting that an ample amount of ideas as well as work have been proposed using the various concepts and theorems in signed networks [7] for the exposure of fruitful observations to the field of social computing. The balance theorem being the heart principle for solving discrepancies in signed networks [8], [9], [2] has a lot of literature works and has been proposed in various forms to solve different challenging problems in social networks. One such work been [10] where the conflicting groups in a signed networks are discovered by involving a novel formulation in which each conflicting group is naturally characterized by the solution to the maximum discrete Rayleigh's quotient (MAX-DRQ) problem.…”