An input to the Clique Problem is a pair (G, N), where G is a graph and N is a positive integer. The question is, does there exist a clique of N vertices in G?

An input to the Subgraph Isomorphism Problem is a pair (G, H) where G and H are undirected graphs.

So a reduction from CP to SI is a function f(G, N) = (G′, H).

Specifically, choose G′ = G and H = a complete graph of N vertices. (A complete graph is one where every vertex is adjacent to every other vertex. That is, it is a clique.)

In graph theory notation, K_N is a complete graph of N vertices. So the reduction is f(G, N) = (G, K_N).