Post-Processing Hierarchical Community Structures: Quality Improvements and Multi-scale View

TL;DR

This paper introduces new methods to enhance hierarchical community detection in networks by optimizing quality functions over broader partitions and enabling multi-scale analysis to identify communities at different levels.

Contribution

It proposes novel optimization techniques for additive quality functions and introduces multi-scale quality functions for detecting communities at multiple levels.

Findings

Optimized a broad class of quality functions over larger partition sets.

Developed multi-scale quality functions for multi-level community detection.

Improved detection of meaningful community structures at various scales.

Abstract

Dense sub-graphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Most existing community detection algorithms produce a hierarchical structure of community and seek a partition into communities that optimizes a given quality function. We propose new methods to improve the results of any of these algorithms. First we show how to optimize a general class of additive quality functions (containing the modularity, the performance, and a new similarity based quality function we propose) over a larger set of partitions than the classical methods. Moreover, we define new multi-scale quality functions which make it possible to detect the different scales at which meaningful community structures appear, while classical approaches find only one partition.