Overlapping Communities Detection via Measure Space Embedding

TL;DR

This paper introduces a fast, parallelizable community detection algorithm that embeds graphs into measure spaces using random walks and applies a modified $k$-means, demonstrating strong performance on benchmarks and theoretical guarantees.

Contribution

The paper proposes a novel measure space embedding approach for overlapping community detection, with a new algorithm that is both efficient and backed by theoretical analysis.

Findings

Outperforms existing algorithms on standard benchmarks.

Achieves linear time complexity in the number of edges.

Provides theoretical guarantees under stochastic block model.

Abstract

We present a new algorithm for community detection. The algorithm uses random walks to embed the graph in a space of measures, after which a modification of $k$-means in that space is applied. The algorithm is therefore fast and easily parallelizable. We evaluate the algorithm on standard random graph benchmarks, including some overlapping community benchmarks, and find its performance to be better or at least as good as previously known algorithms. We also prove a linear time (in number of edges) guarantee for the algorithm on a $p,q$-stochastic block model with $p \geq c\cdot N^{-\frac{1}{2} + \epsilon}$ and $p-q \geq c' \sqrt{p N^{-\frac{1}{2} + \epsilon} \log N}$.