Hi,
I think a great way to make people build their network is to suggest them to groups and people . In this way people will interact more with each other and find groups/people they otherwise wont have searched for.
A tab can be provided on Members page besides "All Members" , "My Friends" - "Friend suggestions"..similarly for Groups page.
These suggestions can be taken by running a query to find friends of friends and groups of friends.
A fancy add on would be facebook like interaction where we can delete suggestions.
Let me know how this sounds.
Thanks.