Maximum Edge-based Quasi-Clique: Novel Iterative Frameworks

2026-01-21

AI Summary

This work addresses the NP-hard problem of efficiently mining the largest γ-quasi-clique satisfying a given edge density threshold in complex networks—a task hindered by the lack of heredity, which impedes scalability to large graphs. The authors propose EQC-Pro, the first algorithm to reformulate this non-hereditary problem into a sequence of hereditary subproblems, enabling an iterative solving framework that supports effective pruning and reduction. A novel heuristic strategy is also introduced to accelerate the search process. Extensive experiments on 253 real-world large-scale graphs demonstrate that EQC-Pro achieves up to four orders of magnitude speedup over state-of-the-art methods, substantially advancing the efficiency of γ-quasi-clique enumeration.

Technology Category

• Search and Optimization: Heuristic Search
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Extracting cohesive subgraphs from complex networks is a fundamental task in graph analytics and is essential for understanding biological, social, and web graphs. The edge-based $\gamma$-quasi-clique model offers a flexible alternative by identifying subgraphs whose edge densities exceed a specified threshold $\gamma$. However, finding the exact maximum edge-based quasi-clique is computationally challenging, as the problem is NP-hard and lacks the hereditary property. These characteristics limit the effectiveness of conventional pruning methods and the development of efficient reduction rules. As a result, existing algorithms, such as QClique and FPCE, struggle to scale to large graphs. In this paper, we revisit the problem and propose a novel iterative framework that reformulates the problem as a sequence of hereditary subproblems, enabling more effective pruning and reduction strategies and improving the worst-case time complexity. Furthermore, we redesign the iterative process and introduce a novel heuristic to further improve practical efficiency. Extensive experiments on 253 large-scale real-world graphs demonstrate that our proposed algorithm EQC-Pro outperforms existing methods by up to four orders of magnitude.

Problem

• maximum edge-based quasi-clique
• graph mining
• NP-hard problem
• cohesive subgraph
• edge density

Innovation

• quasi-clique
• iterative framework
• hereditary subproblem
• graph pruning
• edge density