Graph Compartmentalization

TL;DR

This paper introduces a new measure of graph compartmentalization that is invariant to graph size and structure, enabling better comparison and analysis of large graphs, with applications to political polarization.

Contribution

It proposes a novel, analytically computable measure of graph compartmentalization that outperforms modularity in simulated benchmarks and real-world applications.

Findings

New measure outperforms modularity in simulations

Measure is invariant to graph size and structure

Application demonstrates relevance to political polarization

Abstract

This article introduces a concept and measure of graph compartmentalization. This new measure allows for principled comparison between graphs of arbitrary structure, unlike existing measures such as graph modularity. The proposed measure is invariant to graph size and number of groups and can be calculated analytically, facilitating measurement on very large graphs. I also introduce a block model generative process for compartmentalized graphs as a benchmark on which to validate the proposed measure. Simulation results demonstrate improved performance of the new measure over modularity in recovering the degree of compartmentalization of graphs simulated from the generative model. I also explore an application to the measurement of political polarization.