cliques in G(n,p)
G(n,p) is the random graph model in which there are n nodes and each possible edge appears independently with probability p.
The clique number of a graph is the size of a largest complete
subgraph. Computing the clique number is NP-complete.
In Modern graph theory, page 230, Bollobás shows that the clique number of G(n,p) as n→∞ is almost surely d or d+1, where d is the greatest natural number such that binomial(n,d)*p^binomial(d,2)≥log(n). We have 1≤d<n and d=2*log(n)/log(1/p)+O(loglog(n)).
How accurate is this formula when n is small? I did some simulations to check this.