It may not be necessary for all those people to give LinkedIn access to their email address books. Say you're A and you see a suggestion for B. Maybe a mutual

It may not be necessary for all those people to give LinkedIn access to their email address books. Say you're A and you see a suggestion for B. Maybe a mutual friend C uploaded their email address book, which includes both A and B in it, and LinkedIn's PYMK can use the feature "A and B have a mutual email-network-friend", which might be useful. Given that email address books are really large, only a few of them might give lots of these sorts of second-order connections. Second order connections on the LinkedIn network could be driving these recommendations too. People's friend-of-friends sets can be really large, like typically tens of thousands if I remember right...