Comparing Hierarchical Network Partitions Based on Relative Entropy
Keywords: comparing network partitions, partition similarity, random walk, relative entropy
TL;DR: We develop a link-aware (dis-)similarity measure for hierarchical network partitions based on the description of random walks and the Kullback-Leibler divergence.
Abstract: Networks model the interconnected entities in systems and can be partitioned differently, prompting ways to compare partitions.
Common partition similarity measures, such as the Jaccard index and variants of mutual information, are essentially based on measuring set overlaps.
However, they ignore link patterns which are essential for the organisation of networks.
We propose flow divergence, an information-theoretic divergence measure for comparing (hierarchical) network partitions, inspired by the ideas behind the Kullback-Leibler divergence and the description of random walks.
Flow divergence adopts a coding perspective and compares network partitions $\mathsf{A}$ and $\mathsf{B}$ by considering the expected extra number of bits required to describe a random walk on a network using an estimate $\mathsf{B}$ of the network's assumed true partition $\mathsf{A}$.
We show that flow divergence distinguishes between partitions that traditional measures consider equally good when compared to a reference partition.
Submission Type: Extended abstract (max 4 main pages).
Submission Number: 163
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