Max Number of Paths of Length 2 in a Graph with N Nodes -


what maximum number of unique paths of length 2 in graph n nodes?

a path of length 2 u v u->u0->v (where u0 different vertex in graph). in clique can choose each of n-2 (all u,v) u0.
so have n-2 paths between each 2 nodes - of length 2.
so overall, can choose u , v : choose(2,n) = n!/((n-2)!) , each of them have n-2 possibilities, total: n!*(n-2)/((n-2)!)= n!/((n-3)!)=n*(n-1)*(n-2)


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