1. A method comprising: on a computer-based social networking service, executing computer program instructions which cause one or more computer processors to perform the operations of: receiving input from a first member that indicates a first connection invitation, the first connection invitation a request to connect to a subject member of the social networking service; receiving input from a second member that indicates a second connection invitation, the second connection invitation a request to connect to the subject member of the social networking service; determining a first relevance score for the first member based upon a first plurality of signals gathered by the social networking service, the first relevance score expressing a predicted likelihood that the subject member knows the first member; determining a second relevance score for the second member, based upon a second plurality of signals gathered by the social networking service, the second relevance score expressing a predicted likelihood that the subject member knows the second member; and generating a notification to the subject member of the first and second connection invitations, the notification ordering the first and second connection invitations based upon the first and second respective relevance scores of the first and second members.