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We measure polarization in the United States Congress using the network science concept of modularity. Modularity provides a conceptually-clear measure of polarization that reveals both the number of relevant groups and the strength of inter-group divisions without making restrictive assumptions about the structure of the party system or the shape of legislator utilities. We show that party influence on Congressional blocs varies widely throughout history, and that existing measures underestimate polarization in periods with weak party structures. We demonstrate that modularity is a significant predictor of changes in majority party and that turnover is more prevalent at medium levels of modularity. We show that two variables related to modularity, called `divisiveness and `solidarity, are significant predictors of reelection success for individual House members. Our results suggest that modularity can serve as an early warning of changing group dynamics, which are reflected only later by changes in party labels.
This chapter introduces statistical methods used in the analysis of social networks and in the rapidly evolving parallel-field of network science. Although several instances of social network analysis in health services research have appeared recentl
We represent collaboration of authors in computer science papers in terms of both affiliation and collaboration networks and observe how these networks evolved over time since 1960. We investigate the temporal evolution of bibliometric properties, li
Power grids exhibit patterns of reaction to outages similar to complex networks. Blackout sequences follow power laws, as complex systems operating near a critical point. Here, the tolerance of electric power grids to both accidental and malicious ou
We estimate, from first-principles, the rate of inter-party avalanche involvements. The model suggests that the likelihood of inter-party involvements is quadratic in the density of parties -- twice as many parties quadruples the likelihood. The mode
In this work we consider the topological analysis of symbolic formal systems in the framework of network theory. In particular we analyse the network extracted by Principia Mathematica of B. Russell and A.N. Whitehead, where the vertices are the stat