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.
Highlights
Graph labelling is concerned with the problem of estimating the labels of one or more nodes within a graph, where an association between the graph’s structure and the distribution of labels is assumed to exist
Graph labelling is a fundamental task within network science, with diverse applications
This work builds upon a previously introduced (Glonek et al 2018) semi-supervised graph labelling method using random walks to absorption, the Graph Labelling Semi-Supervised (GLaSS) method, and uses it to analyse a collection of undirected political networks from the United States House of Representatives and Senate
Summary
Graph labelling is concerned with the problem of estimating the labels of one or more nodes within a graph, where an association between the graph’s structure and the distribution of labels is assumed to exist. Many graph labelling algorithms exist, both supervised (Azran 2007; Hassan and Radev 2010; Talukdar et al 2008) and unsupervised (Perozzi et al 2014; Pons and Latapy 2005; Zhou and Lipkowsky 2004). In both approaches, a graph comprises unlabelled and labelled nodes, and the algorithms seek to estimate the labels of the unlabelled nodes. Previous works have examined methods to locate individual politicians within a multidimensional political spectrum (Poole and Rosenthal 1985; 2001), the detection of voting blocs or communities within a political voting network (2019) 4:62
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