Normalizing Interconnected Data: A-A, A-B, B-B

[Spiderman]

This may be a simple problem, but I wanted to run it by some other people before using my solution.

I have two distinct sets of items A and B which may or may not be connected to one another. I want to know whether or not the interconnections between them are significiantly different, i.e are the number of connections between A-A, A-B, and B-B different - are A's connected more to A's, for example. However, there are many more B's than A's. Normally I would just divide the value by the number of items, but how do I do this with interconnected items? Is the normalized value of the number of A-A connections =

number of connections/(A*A)

And similarly for A-B: number of connections/(A*B)

I can't determine if this is right or not.

 

[Rasine]

you may want to do a chi squared goodness of fit test. seeing if a-a matches the data for a-b..ect