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A Parallel Hierarchical Approach for Community Detection on Large-scale Dynamic Networks

Grigoriy Bokov, Aleksandr Konovalov, Anna Uporova, Stanislav Moiseev, Ivan Safonov, Alexander Radionov

TL;DR

The paper tackles dynamic community detection in large-scale networks by introducing LD-Leiden, a parallel Leiden-based algorithm that updates only a local neighborhood and maintains an incrementally updated inner hierarchical graph. By decoupling local moves and performing inner Leiden iterations on a hierarchical structure, LD-Leiden achieves modularity comparable to Leiden while delivering substantial speedups and scalability across diverse networks. Extensive experiments show LD-Leiden outperforms static and dynamic baselines in both single- and multi-threaded settings, with robust performance across batch sizes. This approach enables efficient, real-time tracking of communities in large dynamic networks, with practical implications for social, information, and biological systems.

Abstract

In this paper, we propose a novel parallel hierarchical Leiden-based algorithm for dynamic community detection. The algorithm, for a given batch update of edge insertions and deletions, partitions the network into communities using only a local neighborhood of the affected nodes. It also uses the inner hierarchical graph-based structure, which is updated incrementally in the process of optimizing the modularity of the partitioning. The algorithm has been extensively tested on various networks. The results demonstrate promising improvements in performance and scalability while maintaining the modularity of the partitioning.

A Parallel Hierarchical Approach for Community Detection on Large-scale Dynamic Networks

TL;DR

The paper tackles dynamic community detection in large-scale networks by introducing LD-Leiden, a parallel Leiden-based algorithm that updates only a local neighborhood and maintains an incrementally updated inner hierarchical graph. By decoupling local moves and performing inner Leiden iterations on a hierarchical structure, LD-Leiden achieves modularity comparable to Leiden while delivering substantial speedups and scalability across diverse networks. Extensive experiments show LD-Leiden outperforms static and dynamic baselines in both single- and multi-threaded settings, with robust performance across batch sizes. This approach enables efficient, real-time tracking of communities in large dynamic networks, with practical implications for social, information, and biological systems.

Abstract

In this paper, we propose a novel parallel hierarchical Leiden-based algorithm for dynamic community detection. The algorithm, for a given batch update of edge insertions and deletions, partitions the network into communities using only a local neighborhood of the affected nodes. It also uses the inner hierarchical graph-based structure, which is updated incrementally in the process of optimizing the modularity of the partitioning. The algorithm has been extensively tested on various networks. The results demonstrate promising improvements in performance and scalability while maintaining the modularity of the partitioning.

Paper Structure

This paper contains 32 sections, 3 theorems, 26 equations, 9 figures, 30 tables, 9 algorithms.

Table of Contents

  1. Introduction
  2. Related works
  3. Preliminaries
  4. Graph's Partitioning
  5. Modularity
  6. Static vs Dynamic Graphs
  7. Dynamic Community Detection
  8. Leiden algorithm
  9. Local Dynamic Leiden Algorithm
  10. Experimental Results
  11. Experimental Environment
  12. Baseline Approaches
  13. Experimental Networks
  14. Performance in the single-threaded mode
  15. Dependence on batch update size
  16. ...and 17 more sections

Key Result

Lemma 1

The computational complexity of MoveStage($U$) is where $n \leq d^M |U|$.

Figures (9)

  • Figure 1: Inner graph structure of the LD-Leiden algorithm. The green arrows on each level indicate which nodes are connected by edges. The gray lines represent the parent-child relationship.
  • Figure 2: Decouple process. The boundaries of communities are marked with dashed lines, and their nodes are painted in unique colors. Red crosses indicate the current nodes that are being considered. Red and dashed grey arrows show possible ways to move nodes to other communities. The labels of such arrows indicate modularity increments from the moving of nodes. The red arrows indicate the moves that will be applied.
  • Figure 3: An inner Leiden iteration of the LD-Leiden algorithm. The boundaries of communities are indicated by dashed lines, and their nodes are represented by unique colors. Refined communities are depicted by notches on the nodes. Nodes without notches represent singleton refined communities. Red crosses indicate the affected nodes, blue arrows represent the edges at the current level, and red arrows show possible ways to move nodes to other communities.
  • Figure 4: Runtime in seconds (logarithmic scale) of the single-thread mode for LD-Leiden, Leidenalg, DF-Leiden, NetworKit, Grappolo for each batch update on the networks divided into 100 equal-length batches.
  • Figure 5: Modularity of the single-thread mode for LD-Leiden, Leidenalg, DF-Leiden, NetworKit, Grappolo for each batch update on the networks divided into 100 equal-length batches.
  • ...and 4 more figures

Theorems & Definitions (6)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 1
  • proof