Database

[{"_id":ObjectId("5a934e000102030405000000"),"linkIds":[ObjectId("5a934e000102030405000001"),ObjectId("5a934e000102030405000002"),ObjectId("5a934e000102030405000003")]},{"_id":ObjectId("5a934e000102030405000001"),"linkIds":[ObjectId("5a934e000102030405000002"),ObjectId("5a934e000102030405000004"),ObjectId("5a934e000102030405000006")]},{"_id":ObjectId("5a934e000102030405000002"),"linkIds":[ObjectId("5a934e000102030405000004"),ObjectId("5a934e000102030405000006"),ObjectId("5a934e000102030405000008")]},{"_id":ObjectId("5a934e000102030405000003"),"linkIds":[ObjectId("5a934e000102030405000002"),ObjectId("5a934e000102030405000004"),ObjectId("5a934e000102030405000008")]},{"_id":ObjectId("5a934e000102030405000004"),"linkIds":[ObjectId("5a934e000102030405000001"),ObjectId("5a934e000102030405000003"),ObjectId("5a934e000102030405000005")]},{"_id":ObjectId("5a934e000102030405000005"),"linkIds":[ObjectId("5a934e00010203040500000a"),ObjectId("5a934e00010203040500000b"),ObjectId("5a934e00010203040500000c")]},{"_id":ObjectId("5a934e000102030405000006"),"linkIds":[ObjectId("5a934e000102030405000001"),ObjectId("5a934e000102030405000002"),ObjectId("5a934e00010203040500000a")]},{"_id":ObjectId("5a934e000102030405000007"),"linkIds":[ObjectId("5a934e000102030405000005"),ObjectId("5a934e000102030405000006"),ObjectId("5a934e000102030405000008")]},{"_id":ObjectId("5a934e000102030405000008"),"linkIds":[ObjectId("5a934e000102030405000001"),ObjectId("5a934e000102030405000005"),ObjectId("5a934e00010203040500000b")]},{"_id":ObjectId("5a934e000102030405000009"),"linkIds":[ObjectId("5a934e000102030405000005"),ObjectId("5a934e000102030405000007"),ObjectId("5a934e000102030405000008")]}]

Query

db.collection.aggregate([{"$lookup":{"from":"collection","localField":"linkIds","foreignField":"_id","as":"output"}},{"$project":{"output":{$setDifference:["$linkIds","$output._id"]}}},{$match:{$expr:{$gt:[{$size:"$output"},0]}}}])

Result