I'm aware that Vertex Cover and Independent Set are complements of eachother, but I've also heard Independent Set referred to something in relation to Clique; I just don't recall what. It can't be the complement, because if it is, then Clique and Vertex cover would be the same, wouldn't it?
[Math] the relationship between Clique, Independent Set, and Vertex Cover
graph theory
Best Answer
A set of vertices in a graph $\Gamma$ form a clique iff they form an independent set in the complement of $\Gamma$. Is that what you were looking for?
In response to your comment below: Cliques and independent sets are sets of vertices rather than graphs, so they technically can't be complementary graphs. However, the induced subgraph spanned by a clique is the complement of the induced subgraph spanned by an independent set of the same size.