发现大规模凝聚子图是图挖掘的一项关键任务。现有模型（如团、k-plex 和 γ-准团）采用固定的密度阈值，忽略了连通性随子图规模增大而自然衰减的特性。Flexi-clique 模型通过施加一个随子图规模亚线性增长的度约束，克服了这一局限。本文对 Flexi-clique 进行了算法研究，证明其为 NP-难问题，并分析其非遗传性（non-hereditary）性质。为应对计算挑战，我们提出了两种算法：一是 Flexi-Prune 算法（FPA），一种基于核（core）初始化与连通性感知剪枝的快速启发式算法；二是高效分支限界算法（EBA），一种融合多重剪枝规则的精确求解框架。在大规模真实网络与合成网络上的实验表明，FPA 以显著更低的开销实现近似最优质量，而 EBA 能高效计算精确解。因此，Flexi-clique 为在复杂网络中发现大规模、有意义的子图提供了一种实用且可扩展的建模方法。

Discovering large cohesive subgraphs is a key task for graph mining. Existing models, such as clique, k-plex, and γ-quasi-clique, use fixed density thresholds that overlook the natural decay of connectivity as the subgraph size increases. The Flexi-clique model overcomes this limitation by imposing a degree constraint that grows sub-linearly with subgraph size. We provide the algorithmic study of Flexi-clique, proving its NP-hardness and analysing its non-hereditary properties. To address its computational challenge, we propose the Flexi-Prune Algorithm FPA, a fast heuristic using core-based seeding and connectivity-aware pruning, and the Efficient Branch-and-Bound Algorithm EBA, an exact framework enhanced with multiple pruning rules. Experiments on large real-world and synthetic networks demonstrate that FPA achieves near-optimal quality at much lower cost, while EBA efficiently computes exact solutions. Flexi-clique thus provides a practical and scalable model for discovering large, meaningful subgraphs in complex networks.