Linkedin People You May Know product (Aka Connection suggestion algorithm) uses many features to calculate a connection probability among two people.

Some examples are : companies position overlap (How many months/years both individuals work together at same company, similar/related field) , school education overlap, strong unconnected people in linkedin connection graph. (both individual have many common friends) etc.

The secret sauce is the information linkedin can extract out of all the 500M connections it knows to get the right weight for all the features and train the scoring model. The model gives high accuracy and plenty of "aha" moments for the user.

How do I know ?? I helped built it :)