Correlation between degree of two vertices in a n-vertices graph

[ppftw]

Hi! I'm a bit stumped on this computer-science-related statistics (I think that's what it would fall under) problem. It's over here:

http://math.stackexchange.com/questions/796517/correlation-between-the-degree-of-two-vertices-in-an-undirected-graph/796526?noredirect=1#796526

It would be awesome if someone could modify the answer, confirm it, or suggest an alternative approach...

 

[haruspex]

What is Var of Bin(n-1,p)?
The rest looks ok.

 

[ppftw]

Oh, it should be (n-1)p(1-p). Thanks for catching that and your response.