Locating highly connected clusters in large networks with HyperLogLog counters

TL;DR

This paper presents a memory-efficient method based on HyperLogLog counters to locate highly connected clusters in large networks, aiding community detection with proven performance guarantees.

Contribution

It adapts the HyperBall algorithm to identify dense subgraph regions and evaluates their connectivity measures, offering a novel approach for large-scale network clustering.

Findings

Effective in identifying clustered regions in large graphs

Provides good seed sets for community detection algorithms

Demonstrates strong performance on synthetic and real-world networks

Abstract

In this paper we introduce a new method to locate highly connected clusters in a network. Our proposed approach adapts the HyperBall algorithm to localize regions with a high density of small subgraph patterns in large graphs in a memory-efficient manner. We use this method to evaluate three measures of subgraph connectivity: conductance, the number of triangles, and transitivity. We demonstrate that our algorithm, applied to these measures, helps to identify clustered regions in graphs, and provides good seed sets for community detection algorithms such as PageRank-Nibble. We analytically obtain the performance guarantees of our new algorithms, and demonstrate their effectiveness in a series of numerical experiments on synthetic and real-world networks.