Maximum Edge-based Quasi-Clique: Novel Iterative Frameworks

TL;DR

This paper introduces a new iterative framework for efficiently extracting maximum edge-based quasi-cliques in large graphs, significantly outperforming existing algorithms in scalability and speed.

Contribution

The paper proposes a novel iterative approach that reformulates the problem into hereditary subproblems, enabling better pruning and reduction, and introduces a heuristic for enhanced practical efficiency.

Findings

EQC-Pro outperforms existing algorithms by up to four orders of magnitude.

The new framework effectively scales to large real-world graphs.

Experimental results validate the efficiency and scalability of the proposed method.

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.