K₅, a complete graph. If a subgraph looks like this, the vertices in that subgraph form a clique of size 5.

In graph theory, a clique in an undirected graph G, is a set of vertices V such that for every two vertices in V, there exists an edge connecting the two. This is equivalent to saying that the subgraph induced by V is a complete graph. The size of a clique is the number of vertices it contains. Download high resolution version (827x827, 20 KB) Wikipedia does not have an article with this exact name. ... Download high resolution version (827x827, 20 KB) Wikipedia does not have an article with this exact name. ... A diagram of a graph with 6 vertices and 7 edges. ... This article just presents the basic definitions. ... This article just presents the basic definitions. ... This article just presents the basic definitions. ... In the mathematical field of graph theory a complete graph is a simple graph where an edge connects every pair of vertices. ...

The clique problem refers to the problem of finding the largest clique in any graph G. This problem is NP-complete, and as such, many consider that it is unlikely that an efficient algorithm for finding the largest clique of a graph exists. In computational complexity theory, the clique problem or k-clique problem is a graph-theoretical NP-complete problem. ... In complexity theory, the NP-complete problems are the most difficult problems in NP, in the sense that they are the ones most likely not to be in P. The reason is that if you could find a way to solve an NP-complete problem quickly, then you could use... Diagram of complexity classes provided that P ≠ NP. If P = NP, then all three classes are equal. ...

A k-clique is a clique of size k. Therefore, the k-clique problem refers to the problem of finding a clique of size k, i.e. a complete subgraph G′(V′,E′) of G with |V′|=k. A k-clique can be found using a brute-force algorithm in O(n^k) time. In computer science, the Clique Problem is an NP_complete problem in complexity theory. ... In the mathematical field of graph theory a complete graph is a simple graph where an edge connects every pair of vertices. ...

The opposite of a clique is an independent set. If we already know that the independent set problem is NP-complete, then it is easy to prove, as the size of the largest clique is the same as the size of the largest independent set in the complement graph. In graph theory, an independent, or stable, set in a graph G, which contains vertices V, is a set of vertices V (a subset of V) such that for every two vertices in V, there is no edge connecting the two. ... In graph theory, an independent, or stable, set in a graph G, which contains vertices V, is a set of vertices V (a subset of V) such that for every two vertices in V, there is no edge connecting the two. ... In graph theory, an independent, or stable, set in a graph G, which contains vertices V, is a set of vertices V (a subset of V) such that for every two vertices in V, there is no edge connecting the two. ... In graph theory the complement or inverse of a graph is a graph on the same vertices such that two vertices of are adjacent if and only if they are not adjacent in . ...