Fig. 7: Polarization in the U.S. Congress between 93rd and 114th Congress (1973–2016).

Panels are divided into regions corresponding to subsequent White House administrations with colors denoting Republican (red) and Democratic (blue) presidents. Approximations based on m = 10 leading eigenpairs from both ends of the spectrum were used. All results are reported for both the House of Representatives and the Senate. a Degree of Balance time series based on the Multiscale Semiwalk Balance approach, \(B({\beta }_{\max })\), and Walk Balance of Estrada and Benzi⁴, B(1). b Frustration ratios computed for best partitions into 2 clusters, F(2), general partitions into k clusters, F(B), and partitions based on partisan affiliations, F(P). c Similarity between party-based partitions and best bipartitions, AMI(2, P), as well as best partitions into k clusters, AMI(B, P), using Adjusted Mutual Information (AMI) score²⁹. The closer a value is to 1, the better the match between two clustering solutions. d Numbers of clusters in the solutions minimizing F(B) (left y-axis), as well as the fraction of nodes within the two largest clusters (right y-axis).