I have a min maxed face, but most of her contacts have relatively low connection rating. Anyone have any ideas for how to improve their connection rating?

talk to your GM. you would increase their connection rating the same way you would increase their loyalty: roleplaying.

so, for example, ask your GM if you can go on a run that will improve their connection rating. for example, maybe someone higher up in the mafia wants something and they give a mafia contact of yours a chance to get it for them. that contact asks you if you will help them out as a favor. and blammo, there you have it: instant contact connectivity boost (gets a promotion out of it or such).

The beautiful thing about helping your contact up the ranks in there organisation is that not only do you get a contact with a higher connection rating, they will probably also be great full for the assistance, higher loyalty ratting.

Edward

And if you don't get a higher loyalty rating out of it, you'll have some good blackmail if ever push comes to shove.