在计算复杂度理论中，分团问题（clique problem）是图论中的一个NP完全（NP-complete）问题。

clique是一个图中两两相邻的一个点集，或是一个完全子图（complete subgraph），如右图中的1、2、5三个点。

clique problem是问一个图中是否有大小是k以上的clique。任意挑出k个点，我们可以简单的判断出这k个点是不是一个clique，所以这个问题属于NP。

证明这问题是NP完备，我们可以很简单的将独立顶点集问题（Independent set problem)归约成这个问题。因为存在一个大小是k以上的分团，等价于它的补图中存在一个大小是k以上的独立集。

In computer science, the clique problem refers to computational problems of finding cliques (subsets of vertices, all adjacent to each other, also called complete subgraphs) in a graph.

For example, the maximum clique problem arises in the following real-world setting. Consider a social network, where the graph’s vertices represent people, and the graph’s edges represent mutual acquaintance. To find a largest subset of people who all know each other, one can systematically inspect all subsets, a process that is too time-consuming to be practical for social networks comprising more than a few dozen people. Although this brute-force search can be improved by more efficient algorithms, all of these algorithms take exponential time to solve the problem. Therefore, much of the theory about the clique problem is devoted to identifying special types of graph that admit more efficient algorithms, or to establishing the computational difficulty of the general problem in various models of computation. Along with its applications in social networks, the clique problem also has many applications in bioinformatics and computational chemistry.