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.
KeywordsNetwork visualization Signed networks Structural balance Spectral theory
- 5.Bonchi, F., Galimberti, E., Gionis, A., Ordozgoiti, B., Ruffo, G.: Discovering polarized communities in signed networks. In: Proceedings of the 2019 ACM on Conference on Information and Knowledge Management. ACM (2019)Google Scholar
- 7.Coleman, T., Saunderson, J., Wirth, A.: A local-search 2-approximation for 2-correlation-clustering. In: European Symposium on Algorithms, pp. 308–319 (2008)Google Scholar
- 8.Coleman, T., Saunderson, J., Wirth, A.: Spectral clustering with inconsistent advice. In: Proceedings of the 25th International Conference on Machine Learning, pp. 152–159. ACM (2008)Google Scholar
- 10.Easley, D., Kleinberg, J.: Positive and negative relationships. In: Networks, Crowds, and Markets: Reasoning about a Highly Connected World, Cambridge University Press (2010)Google Scholar
- 15.Kaufmann, M., Wagner, D.: Drawing graphs: methods and models, vol. 2025. Springer (2003)Google Scholar
- 17.Kunegis, J., Schmidt, S., Lommatzsch, A., Lerner, J., De Luca, E.W., Albayrak, S.: Spectral analysis of signed graphs for clustering, prediction and visualization. In: Proceedings of the 2010 SIAM International Conference on Data Mining, pp. 559–570. SIAM (2010)Google Scholar
- 18.Leskovec, J., Huttenlocher, D., Kleinberg, J.: Signed networks in social media. In: Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, pp. 1361–1370. ACM (2010)Google Scholar
- 19.Ordozgoiti, B., Gionis, A.: Reconciliation k-median: clustering with non-polarized representatives. In: The World Wide Web Conference, pp. 1387–1397. ACM (2019)Google Scholar
- 20.Redner, S.: Social balance on networks: the dynamics of friendship and hatred. In: APS Meeting Abstracts (2006)Google Scholar