I'm wondering whether I could determine the expected value for the diameter of a random graph given the distribution of the degree of the vertices.
Specifically I have a network of computers that open random connections to each other. I know that each computer attempts to keep a minimum size $k$ connection pool open at all times, but it may also receive incoming connections. The connection graph therefore is not $k$-regular. I'd like to know what the expected diameter of that network would be.