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Advanced Graph Clustering Methods: A Comprehensive and In-Depth Analysis

Timothé Watteau, Aubin Bonnefoy, Simon Illouz-Laurent, Joaquim Jusseau, Serge Iovleff

TL;DR

This paper surveys graph clustering from foundational graph theory and matrix representations to traditional methods (Spectral Clustering, SBM, MCL, Leiden) and modern deep graph clustering techniques (GAE, ARGA, MVGRL). It emphasizes how Laplacian spectra, probabilistic block models, and contrastive/adversarial learning enable effective node partitioning in graphs, supported by empirical comparisons on standard datasets. Key contributions include a structured taxonomy of methods, detailed algorithmic descriptions, and an analysis of performance across metrics such as ACC, NMI, ARI, and modularity, highlighting that the best approach depends on the target objective. The work underlines practical implications for large-scale graphs, multi-view data, and self-supervised learning, pointing to scalability and integration of heterogeneous relations as promising directions for future graph clustering research.

Abstract

Graph clustering, which aims to divide a graph into several homogeneous groups, is a critical area of study with applications that span various fields such as social network analysis, bioinformatics, and image segmentation. This paper explores both traditional and more recent approaches to graph clustering. Firstly, key concepts and definitions in graph theory are introduced. The background section covers essential topics, including graph Laplacians and the integration of Deep Learning in graph analysis. The paper then delves into traditional clustering methods, including Spectral Clustering and the Leiden algorithm. Following this, state-of-the-art clustering techniques that leverage deep learning are examined. A comprehensive comparison of these methods is made through experiments. The paper concludes with a discussion of the practical applications of graph clustering and potential future research directions.

Advanced Graph Clustering Methods: A Comprehensive and In-Depth Analysis

TL;DR

This paper surveys graph clustering from foundational graph theory and matrix representations to traditional methods (Spectral Clustering, SBM, MCL, Leiden) and modern deep graph clustering techniques (GAE, ARGA, MVGRL). It emphasizes how Laplacian spectra, probabilistic block models, and contrastive/adversarial learning enable effective node partitioning in graphs, supported by empirical comparisons on standard datasets. Key contributions include a structured taxonomy of methods, detailed algorithmic descriptions, and an analysis of performance across metrics such as ACC, NMI, ARI, and modularity, highlighting that the best approach depends on the target objective. The work underlines practical implications for large-scale graphs, multi-view data, and self-supervised learning, pointing to scalability and integration of heterogeneous relations as promising directions for future graph clustering research.

Abstract

Graph clustering, which aims to divide a graph into several homogeneous groups, is a critical area of study with applications that span various fields such as social network analysis, bioinformatics, and image segmentation. This paper explores both traditional and more recent approaches to graph clustering. Firstly, key concepts and definitions in graph theory are introduced. The background section covers essential topics, including graph Laplacians and the integration of Deep Learning in graph analysis. The paper then delves into traditional clustering methods, including Spectral Clustering and the Leiden algorithm. Following this, state-of-the-art clustering techniques that leverage deep learning are examined. A comprehensive comparison of these methods is made through experiments. The paper concludes with a discussion of the practical applications of graph clustering and potential future research directions.
Paper Structure (77 sections, 58 equations, 20 figures, 4 tables, 7 algorithms)

This paper contains 77 sections, 58 equations, 20 figures, 4 tables, 7 algorithms.

Table of Contents

  1. Introduction
  2. Background and Definitions
  3. Graph Theory
  4. Definitions
  5. Matrix Representation
  6. Adjacency Matrix
  7. Degree Matrix
  8. Normalized adjacency Matrix
  9. Laplacian Matrix
  10. Graph Clustering
  11. Clustering Evaluation
  12. Supervised Evaluations
  13. Accuracy
  14. Normalized Mutual Information
  15. Adjusted Rand Index
  16. ...and 62 more sections

Figures (20)

  • Figure 1: Graph with eight nodes and nine edges
  • Figure 2: Graph clustering with three clusters
  • Figure 3: Example of a situation where the minimum cut does not provide the optimal solution leskovec2019
  • Figure 4: Comparison between cut score and conductance metrics leskovec2019
  • Figure 5: Single neuron operation
  • ...and 15 more figures