[{"from":"jerry","to":"lois"},{"from":"lois","to":"jerry"},{"from":"superman","to":"lois"},{"from":"lois","to":"superman"}]

db.collection.aggregate([{$graphLookup:{from:"collection",startWith:"$to",connectFromField:"from",connectToField:"from",depthField:"connects",as:"connections"}},{"$match":{"$and":[{from:"superman"},{$or:[{"connections.to":"jerry"},{to:"jerry"}]}]}},{$project:{degreeOfSeparation:{$size:"$connections"}}}])