How can I count the numbers of $r$-cliques in a graph? In other words, the number of triangles, the number of $K_4$, the number of $K_5$ etc. I have tried for example FindClique[G,{4},All], which finds all "isolated" $K_4$s but does not find $K_4$s in a larger clique. So for example if $G = K_5$ then FindClique[G,{4},All] does not find the 4-cliques within G but FindClique[G,{5},All] does find the 5-clique. Is there a simple way of doing this with a Mathematica command or is it necessary to compute the number of smaller cliques from the number of larger cliques?
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