In computer science, the clique problem refers to any of the problems related to finding particular complete subgraphs ("cliques") in a graph, i.e., sets of elements where each pair of elements is connected.
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.
en.wikipedia.org/wiki/Clique_(graph_theory)
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