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单词 Maximal clique
释义

Maximal clique

中文百科

团 (图论) Clique (graph theory)

(重定向自Maximal clique)

在图论领域的一个无向图中,满足两两之间有边连接的顶点的集合,被称为该无向图的团。团是图论中的基本概念之一,用在很多数学问题以及图的构造上。计算机科学中也有对它的研究,尽管在一个图中寻找给定大小的团达到了NP完全的难度,人们还是研究过很多寻找团的算法。

虽然对完全子图的研究可以追溯到Erdős & Szekeres (1935)中拉姆齐理论对图理论的重组,“团”这一术语本身其实源自 Luce & Perry (1949),那篇文章中社会网络的完全子图被用来模拟一“团”人,也就是一组两两相互认识的人。团在科学领域特别是在生物信息学中有许多其他应用。

英语百科

Clique (graph theory) 团 (图论)

(重定向自Maximal clique)
A graph with 23 × 1-vertex cliques (the vertices),42 × 2-vertex cliques (the edges),19 × 3-vertex cliques (light and dark blue triangles), and2 × 4-vertex cliques (dark blue areas).
The 11 light blue triangles form maximal cliques. The two dark blue 4-cliques are both maximum and maximal, and the clique number of the graph is 4.
El grafo completo K5. En un subgrafo como éste, los vértices forman un clique de tamaño 5.
Exemple de graphe possédant une 3-clique (en rouge) : les trois sommets de ce sous-graphe sont tous adjacents deux-à-deux.
Exemple de « biclique » : le graphe biparti complet **,3.

In the mathematical area of graph theory, a clique (/ˈklk/ or /ˈklɪk/) is a subset of vertices of an undirected graph such that its induced subgraph is complete; that is, every two distinct vertices in the clique are adjacent. Cliques are one of the basic concepts of graph theory and are used in many other mathematical problems and constructions on graphs. Cliques have also been studied in computer science: the task of finding whether there is a clique of a given size in a graph (the clique problem) is NP-complete, but despite this hardness result, many algorithms for finding cliques have been studied.

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更新时间:2025/6/17 9:24:56