# Semi-supervised graph labelling reveals increasing partisanship in the United States Congress

## TL;DR

This paper introduces an enhanced semi-supervised graph labelling method, GLaSS, which accurately models political networks and uncovers a rising trend of partisanship in the US Congress over many decades.

## Contribution

The paper refines and applies the GLaSS method to political networks, demonstrating its effectiveness and revealing increasing partisanship in US legislative bodies.

## Key findings

- GLaSS accurately estimates labels in political networks.
- The analysis shows a significant increase in partisanship over time.
- GLaSS outperforms existing labelling methods in this context.

## Abstract

Graph labelling is a key activity of network science, with broad practical applications, and close relations to other network science tasks, such as community detection and clustering. While a large body of work exists on both unsupervised and supervised labelling algorithms, the class of random walk-based supervised algorithms requires further exploration, particularly given their relevance to social and political networks. This work refines and expands upon a new semi-supervised graph labelling method, the GLaSS method, that exactly calculates absorption probabilities for random walks on connected graphs. The method models graphs exactly as discrete-time Markov chains, treating labelled nodes as absorbing states. The method is applied to roll call voting data for 42 meetings of the United States House of Representatives and Senate, from 1935 to 2019. Analysis of the 84 resultant political networks demonstrates strong and consistent performance of GLaSS when estimating labels for unlabelled nodes in graphs, and reveals a significant trend of increasing partisanship within the United States Congress.