What is the proof that the Clique Problem is NP-complete?

The proof that the Clique Problem is NP-complete involves showing that it is both in the NP complexity class and that it is as hard as any problem in NP. This is typically done by reducing a known NP-complete problem, such as the SAT problem, to the Clique Problem in polynomial time. This reduction demonstrates that if a polynomial-time algorithm exists for the Clique Problem, then one also exists for the known NP-complete problem, which implies that the Clique Problem is NP-complete.