A Spectral Algorithm with Additive Clustering for the Recovery of Overlapping Communities in Networks

TL;DR

This paper introduces a spectral clustering algorithm that effectively detects overlapping communities in networks by leveraging spectral properties of the expected adjacency matrix, with proven consistency and good empirical performance.

Contribution

It proposes a novel spectral algorithm with additive clustering for overlapping community detection, including an adaptive version that does not need prior knowledge of the number of communities.

Findings

Algorithm performs well on simulated data

Algorithm effectively detects overlapping communities in real-world graphs

Proven to be consistent under certain degree conditions

Abstract

This paper presents a novel spectral algorithm with additive clustering designed to identify overlapping communities in networks. The algorithm is based on geometric properties of the spectrum of the expected adjacency matrix in a random graph model that we call stochastic blockmodel with overlap (SBMO). An adaptive version of the algorithm, that does not require the knowledge of the number of hidden communities, is proved to be consistent under the SBMO when the degrees in the graph are (slightly more than) logarithmic. The algorithm is shown to perform well on simulated data and on real-world graphs with known overlapping communities.