Graph Theory Help: Finding # of Graphs w/ n Vertices & k Edges

[erogol]

The graph theory HELP!

How many distinct graphs can be found by the set V={1,2,...,n} with k edges?

For this question i conclude that totao.l number of distinct graphs comes with 2^(choose two in n)

but i cannot find the solution which gives the relation with k edges can you help me?

 

[Preno]

There are a total of (n^2 - n)/2 = 1/2 n(n-1) pairs of vertices. You pick k out of these, so you have Comb(1/2 n(n-1), k) possibilities.

If you're talking about directed graphs, multiply this by 2. If you allow for loops, take 1/2 n^2 instead of 1/2 n(n-1).