When characterizing the cohesion of a subgraph, many cohesive subgraph models impose various constraints on the relationship between the minimum degree of vertices and the number of vertices in the subgraph. However, the constraints imposed by the clique, quasi-clique and k-core models are so rigid that they cannot simultaneously characterize cohesive subgraphs of various scales in a graph. This paper characterizes the flexibility of a cohesive subgraph model by the constraint it imposes on this relationship and proposes f -constraint core (f -CC), a new model that can flexibly characterize cohesive subgraphs of different scales. We formalize the FlexCS problem that finds r representative f -CCs in a graph that are most diversified. This problem is NP-hard and is even NP-hard to be approximated within |V |^1−𝜖 for any 𝜖 > 0. To solve the problem efficiently, a divide-and-conquer algorithm is proposed together with some effective techniques including f -CC generation, sub-problem filtering, early termination, and index-based connected component retrieval. Extensive experiments verify the flexibility of the f -CC model and the effectiveness of the proposed algorithm.

在表征子图的内聚性时，许多内聚子图模型对子图中顶点的最小度数和顶点数之间的关系施加了各种约束。然而，clique、quasi-clique 和k -core 模型施加的约束非常严格，以至于它们无法同时表征图中各种尺度的内聚子图。本文通过对这种关系施加的约束来表征内聚子图模型的灵活性，并提出了f -constraint core ( f -CC )，一种可以灵活表征不同尺度的内聚子图的新模型。我们将找到r代表f的FlexCS问题形式化-图表中最多样化的CC。这个问题是 NP 难的，甚至是 NP 难在 | 中被逼近的。V | ^{1− 𝜖}对于任何𝜖 > 0。为了有效地解决问题，提出了一种分治算法以及一些有效的技术，包括f -CC 生成、子问题过滤、提前终止和基于索引的连通分量检索. 大量实验验证了f -CC 模型的灵活性和所提出算法的有效性。