An excerpt from the paper:
We use the implicit social graph to identify clusters of contacts who form groups that are meaningful and useful to each user.I like the idea of using e-mail, mobile, and messaging contacts as an implicit social network. One problem has always been that the implicit social network can be noisy in embarrassing ways. As this paper discusses, using it only for suggesting friends is forgiving and low-risk while still being quite helpful. Another possible application might be to make it easier to share content with people who might be interested.
The Google Mail implicit social graph is composed of billions of distinct nodes, where each node is an email address. Edges are formed by the sending and receiving of email messages ... A message sent from a user to a group of several contacts ... [is] a single edge ... [of] a directed hypergraph. We call the hypergraph composed of all the edges leading into or out of a single user node that user's egocentric network.
The weight of an edge is determined by the recency and frequency of email interactions .... Interactions that the user initiates are [considered] more significant .... We are actively working on incorporating other signals of importance, such as the percentage of emails from a contact that the user chooses to read.
"Don't forget Bob" ... [suggests] recipients that the user may wish to add to the email .... The results ... are very good - the ratio between the number of accepted suggestions and the number of times a suggestion was shown is above 0.8. Moreover, this precision comes at a good coverage ... more than half of email messages.
"Got the wrong Bob" ... [detects] inclusion of contacts in a message who are unlikely to be related to the other recipients .... Almost 70% of the time [it is shown] ... users accept both suggestions, deleting the wrong Bob and adding the correct one.
For more on what Google does with how you use e-mail to make useful features, you might also be interested in another Google paper, "The Learning Behind Gmail Priority Inbox" (PDF).
For more on implicit social networks using e-mail contacts, please see my 2008 post, "E-mail as the social network".