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Signed networks and balance theory provide a natural setting for real-worldscenarios that show polarization dynamics, positive/negative relationships, andpolitical partisanship. For example, they have been proven effective instudying the increasing polarization of the votes in the two chambers of theU.S. Congress from World War II on.  To provide further insights into this particular case study, we propose theapplication of a pipeline to analyze and visualize a signed graph'sconfiguration based on the exploitation of the corresponding Laplacian matrix'spectral properties. The overall methodology is comparable with others based onthe frustration index, but it has at least two main advantages: first, itrequires a much lower computational cost; second, it allows for a quantitativeand visual assessment of how arbitrarily small subgraphs (even single nodes)contribute to the overall balance (or unbalance) of the network.  The proposed pipeline allows the exploration of polarization dynamics shownby the U.S. Congress from 1945 to 2020 at different resolution scales. In fact,we are able to spot and point out the influence of some (groups of) congressmenin the overall balance, as well as to observe and explore polarization'sevolution of both chambers across the years.

Analyzing and visualizing polarization and balance with signed networks: the U.S. Congress case study