How to adjust for group size when analyzing interactions among group members? Consider interactions between members of two distinct groups. If one group has substantially fewer members than the other, then interactions between that group and the larger group will be naturally more frequent than interactions between two members of that same group.
Is there a way to take this into account when analyzing the interactions for frequency and duration of the interaction?
Not quite sure where to start with this question.
EDIT 1
I have two distinct groups which can interact with each other. One of the groups is a lot larger than the other group. The members of the group can interact with each other or with members of the other group. 
I'd like to know if either group particularly favours interaction with the other group and if interactions between members of different groups last longer than interactions between members of the same group.
As one group is a lot larger than the other group, if a certain member had an equal chance of interacting with ANY member of ANY group then I would observe a lot more interactions between members of the small group with members of the large group than interactions between members of the small group. This would possibly lead me to the conclusion that interactions between the groups  are more likely to occur, even though we said at the start that there is a completely even chance of interactions occurring between any member of any group.
How do I factor this into calculations?
Edit 2
The data is yet to be collected. I will be able to record the type and duration of any interactions as well as if the interaction occurred between groups or within either group. I can not identify individuals, only which group they belong to. 
Initially I'm interested in the frequency of interactions, but further down the line it might be useful to look at the duration of the interaction too.
I plan to extend conclusions to a larger population. I plan to compare the results from these 2 groups to results I get from a different 2 groups. I'd like to try and identify factors influencing the willingness to interact between groups rather than within the group.
 A: Regarding the frequency of interaction between groups, based on the assumption in your first edit, let us determine the probability that the member is from group 2 given a member from group 1 socializes with another member.
You are assuming each person encountered to socialize with is selected at random from all the members of both groups combined.  So if $N_1$ is the number of members in group 1 and $N_2$ is the number of members in group 2, the probability that a member from group 1 will socialize with a member from group 2 is $p_{12}=N_2/(N_1+N_2-1)$.  The reason for the $-1$ in the denominator is that the member cannot socialize with himself.
Similarly, the probability that a member from group 2 will socialize with a member from group 1 is $p_{21}=N_1/(N_1+N_2-1)$.
So suppose $N_2=3N_1$ then $p_{12}= 3N_1/(4N_1-1)$ (close to $3/4$). On the other hand $p_{21}= N_1/(4N_1-1)$ (close to $1/4$).  So when the group sizes are very unbalanced the probability that someone from group 1 will match up with someone from group 2 is much larger than the probability that he will match up with someone from his own group as you surmised.
If you want to look at the time to match up with a member from the other group you have to make some assumptions about the sequence of socializations and the time between each encounter.
