Leveraging concept-cognitive learning to identify maximum s-defective cliques in network systems

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Detecting maximum s -defective cliques and cohesive subgraphs tolerating up to s missing edges is crucial for analyzing noisy and dynamic networks, but due to its NP-hardness, it remains challenging, leading to poor time efficiency and difficulties in dynamic scenarios. To address this problem, this study introduces a novel framework that leverages Formal Concept Analysis (FCA) under the paradigm of Concept-Cognitive Learning (CCL). This paper presents a theoretical proof that any maximum s -defective clique can be derived by expanding an equiconcept, which refers to a clique structure with equal intension and extension, and with at most s vertices, thereby ensuring detection completeness. Based on this, we develop two algorithms: a static method SFDC and an incremental method IFDC. Experiments on real-world datasets demonstrate that our approach typically achieves 10x to 100x speedups over state-of-the-art methods in both static and dynamic settings, with particularly strong performance in high-defect and dynamic environments. A case study further illustrates the practical utility of our method in extracting meaningful cohesive structures from real networks.