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Updated: Jul 25, 2025

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(p,q)-biclique counting and enumeration for large sparse bipartite graphs.

Jianye Yang1, Yun Peng1, Dian Ouyang1

  • 1Guangzhou University, Guangzhou, China.

The VLDB Journal : Very Large Data Bases : a Publication of the VLDB Endowment
|June 26, 2023
PubMed
Summary

This study introduces BCList++ for efficient biclique counting in large bipartite graphs, significantly outperforming existing methods. An extension, IUBCList, handles uncertain graphs, offering substantial speedups.

Keywords:
(Branch-and-bound algorithmPruning techniques

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Area of Science:

  • Graph Theory and Algorithms
  • Computational Mathematics
  • Data Mining and Network Analysis

Background:

  • Bipartite graphs are fundamental structures in various applications, including network analysis and machine learning.
  • Efficiently counting and enumerating bicliques (complete subgraphs) is crucial for tasks like graph neural network (GNN) optimization and densest subgraph detection.
  • Existing methods struggle with scalability and efficiency for large, sparse bipartite graphs, lacking effective solutions for biclique enumeration.

Purpose of the Study:

  • To develop efficient algorithms for counting and enumerating (p, q)-bicliques in large sparse bipartite graphs.
  • To propose an advanced method, BCList++, that improves upon baseline approaches by reducing computational complexity.
  • To extend biclique enumeration techniques to uncertain bipartite graphs using an efficient method, IUBCList.

Main Methods:

  • Introduced BCList, a branch-and-bound algorithm with pruning techniques for biclique enumeration.
  • Developed BCList++, employing a layer-based exploration strategy and a cost model for optimized biclique enumeration.
  • Proposed IUBCList, building on BCList++ with pruning techniques for handling uncertain bipartite graphs.

Main Results:

  • BCList++ demonstrated significant performance improvements, outperforming baseline methods by up to three orders of magnitude on real-world datasets.
  • The cost model in BCList++ effectively guides the selection of computation layers, enhancing efficiency.
  • IUBCList achieved substantial speedups, outperforming baseline methods by up to two orders of magnitude on uncertain bipartite graphs.

Conclusions:

  • BCList++ provides a scalable and efficient solution for (p, q)-biclique counting and enumeration in large sparse bipartite graphs.
  • The developed methods, particularly BCList++ and IUBCList, offer significant advancements in computational graph theory.
  • The findings highlight the potential of biclique analysis for optimizing graph neural networks and other complex network applications.