On a given set of n vertices, how many (labelled) graphs contain exactly m edges? Note that (Cr)C is to be interpreted as (n choose r) and (n choose r) is equal to (n choose (n-r)). If x = (n choose m), then (n choose x) = (n choose (x-m)) * m!
Added by Theodore V.
Step 1
The number of possible edges in a complete graph is given by the formula (n choose 2), which is equal to n(n-1)/2. Therefore, the number of ways to choose m edges from this set is (n(n-1)/2) choose m. Show more…
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