We’ve talked about being able to mark a connection attempt as spam and about a “rate the connection” slider, which goes from “obvious spam” on the left, to “close family member” on the right. This implies a confidence rating that can be stored on the connection edge (actually two, since each participant can rate the connection differently). If there can be zero or negative rated connections, then we could filter those from showing in the UI, but still store them to remember that the person gave them a negative rating in case they try to connect again.
Graph analysis and exploring could take into account confidence ratings when it decides which paths to include or show.
Instead of a remove operation, there would be an operation to update the confidence for your half of the connection (each participant in a connection can rate it differently). If there are reasons/flags for the rating, they could be stored on connection edge.
Some flags can warn other users (such as “deceased” or “duplicate”), while others (like "I don’t remember who this is) only affect the confidence rating and inform the user that created them.