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arXiv · 2601.14619

Maximum Edge-based Quasi-Clique: Novel Iterative Frameworks

Hongbo Xia·Shengxin Liu·Zhaoquan Gu
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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 $γ$-quasi-clique model offers a flexible alternative by identifying subgraphs whose edge densities exceed a specified threshold $γ$. 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.

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Hongbo Xia, Shengxin Liu, Zhaoquan Gu. 2026-01-21. Maximum Edge-based Quasi-Clique: Novel Iterative Frameworks. https://arxiv.org/abs/2601.14619

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