[{"from":"jerry","to":"lois"},{"from":"lois","to":"jerry"},{"from":"superman","to":"lois"},{"from":"lois","to":"superman"},{"from":"lois","to":"reporter 1"},{"from":"reporter 1","to":"informant 1"},{"from":"informant 1","to":"bad guy 1"},{"from":"bad guy 1","to":"superman"}]

db.collection.aggregate([{"$match":{"from":"jerry"}},{$graphLookup:{from:"collection",startWith:"$to",connectFromField:"to",connectToField:"from",depthField:"depth",as:"connections"}},{"$set":{"allDegsOfSep":{"$map":{"input":{"$filter":{"input":"$connections","as":"conn","cond":{"$eq":["$$conn.to","superman"]}}},"as":"toSuperman","in":{"$sum":[{"$toInt":"$$toSuperman.depth"},/** +1 zero-based, +1 "to" field*/2]}}}}},{"$project":{"_id":0,"allDegsOfSep":1,"degreeOfSeparation":{"$min":"$allDegsOfSep"}}}])