Visualizing Structural Balance in Signed Networks

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. Structural-balance-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

Bounded Confidence under Preferential Flip: A Coupled Dynamics of Structural Balance and Opinions

In this work we study the coupled dynamics of social balance and opinion formation. We propose a model where agents form opinions under bounded confidence, but only considering the opinions of their friends. The signs of social ties -friendships and enmities- evolve seeking for social balance, taking into account how similar agents' opinions are. We consider both the case where opinions have one and two dimensions. We find that our dynamics produces the segregation of agents into two cliques, with the opinions of agents in one clique differing from those in the other. Depending on the level of bounded confidence, the dynamics can produce either consensus of opinions within each clique or the coexistence of several opinion clusters in a clique. For the uni-dimensional case, the opinions in one clique are all below the opinions in the other clique, hence defining a "left clique" and a "right clique". In the two-dimensional case, our numerical results suggest that the two cliques are separated by a hyperplane in the opinion space. We also show that the phenomenon of unidimensional opinions identified by DeMarzo, Vayanos and Zwiebel (Q J Econ 2003) extends partially to our dynamics. Finally, in the context of politics, we comment about the possible relation of our results to the fragmentation of an ideology and the emergence of new political parties.Comment: 8 figures, PLoS ONE 11(10): e0164323, 201