Clique percolation algorithm

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I have searched for long time and I couldn't realize what is the best way for finding clique percolation. As I see it, there are 2 methods

  1. Find cliques of size k in graph G and then create a graph between adjacent clique nodes.
  2. Find maximal cliques of size >= k-1 and then create a graph between adjacent clique nodes.

Well as I know finding max-cliques is NP-Complete problem, and as I have understood finding k clique in graph G is polynomial, so is the first method is more efficient? I'd be happy if someone can help and clarify the issue, Thank you.

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