Friends of Friends

Probability Level 1

Here is a network graph constructed with data from Facebook of 20 people and all of the mutual friendship connections among them. Clearly Barbie has the most friends to invite to her parties (9), but if invitations go out not only to friends but also to all friends of friends, then whose party will have the most invites?

Notes and assumptions

Each dot represents a person.
Each line represents mutual friendship between the people on either end .