LinkedIn definitely uses same IP address to suggest connections. My wife as suggested connection really stood up in this way for many reasons (profile recently created, a few connections from the other side of the world and in a totally different industry).

But you probably have your wife in your contacts.

So it would be even worse, they would need to retrieve a phone number in some way and match that. I don't register email contacts anywhere, and I am not using the LinkedIn app. I would say that I have seen similar things at work/work location (consultant). Seeing people with no shared contacts among the first ones in the suggested list. Until then I though it was related to 2nd or 3rd level of linkage.

They most certainly do. In fact, they're worse than Facebook in many areas - particularly in their blatant disregard for privacy.

LinkedIn doesn't even pretend to have any sense of privacy.

Neither does Facebook.

Unfortunately, both do pretend.