Remove all leafs from graph - mongodb

Question

I've built a relations graph in a MongoDB collection, for example:
{ "user_id": 1, "follower_id": 2 }
{ "user_id": 1, "follower_id": 3 }
{ "user_id": 2, "follower_id": 1 }
{ "user_id": 2, "follower_id": 3 }
{ "user_id": 3, "follower_id": 4 }
{ "user_id": 5, "follower_id": 2 }
This represents a directed graph like this:
Is there an efficient way to remove "leafs" from the graph? In the example I'd like to remove node 4 from the graph, because that node only has one link with node 3 and remove node 5 because only node 2 links to it.
Or to say it with graph terminology: only keep vertices with indegree > 1 or outdegree > 1

Answer 1

Short answer would be no - there is no efficient way to do what you want with schema like this. It can be by iterating over all nodes, for example using aggregation framework, and removing nodes as separate operation but I think it is all what can be done. Assuming nodes are in graph collection it could be something like below but it is far from effective:
db.graph.aggregate(
{$project: {index: {$const: [0, 1]}, user_id: 1, follower_id: 1}},
{$unwind: "$index"},
{$project: {id: {$cond: [{$eq: ["$index", 0 ]}, "$user_id", "$follower_id"]} }},
{$group: {_id: "$id", count: {$sum: 1}}},
{$match: {count: {$lte: 1}}}
).result.forEach(function(node) { db.graph.remove({user_id: node._id});})
You could use more document-like schema if you want operations like this to be efficient.
{
user_id: 1,
follows: [2, 3],
followed_by: [2]
}