Find all complete sub-graphs within a graph

Question

Is there a known algorithm or method to find all complete sub-graphs within a graph? I have an undirected, unweighted graph and I need to find all subgraphs within it where

Answer 1

Well the problem of finding a k-vertex subgraph in a graph of size n is of complexity

O(n^k k^2)

Since there are n^k subgraphs to check and each of them have k^2 edges.

What you are asking for, finding all subgraphs in a graph is a NP-complete problem and is explained in the Bron-Kerbosch algorithm listed above.