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Graph Compartmentalization

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.