Neo4j Cypher find two disjoint nodes

Question

I'm using Neo4j to try to find any node that is not connected to a specific node "a". The query that I have so far is:

MATCH p = shortestPath((a:Node {id:"123"})-[*]-(b:Node))
WHERE p IS NULL
RETURN b.id as b

So it tries to find the shortest path between a and b. If it doesn't find a path, then it returns that node's id. However, this causes my query to run for a few minutes then crashes when it runs out of memory. I was wondering if this method would even work, and if there is a more efficient way? Any help would be greatly appreciated!

edit:

MATCH (a:Node {id:"123"})-[*]-(b:Node),
(c:Node)
WITH collect(b) as col, a, b, c
WHERE a <> b AND NOT c IN col
RETURN c.id 

So col (collect(b)) contains every node connected to a, therefore if c is not in col then c is not connected to a?

Answer 1

For one, you're giving this MATCH an impossible predicate to fulfill, so it will never find the shortest path.

WHERE clauses are associated with MATCH, OPTIONAL MATCH, and WITH clauses, so your query is asking for the shortest path where the path doesn't exist. That will never return anything.

Also, the shortestPath will start at the node you DON'T want to be connected, so this has no way of finding the nodes that aren't connected to it.

Probably the easiest way to approach this is to MATCH to all nodes connected to your node in question, then MATCH to all :Nodes checking for those that aren't in the connected set. That means you won't have to do a shortestPath from every single node in the db, just a membership check in a collection.

You'll need APOC Procedures for this, as it has the fastest means of matching to nodes within a subgraph.

MATCH (a:Node {id:"123"})
CALL apoc.path.subgraphNodes(a, {}) YIELD node
WITH collect(node) as subgraph
MATCH (b:Node)
WHERE NOT b in subgraph
RETURN b.id as b

EDIT

Your edited query is likely to blow up, that's going to generate a huge result set (the query will build a result set of every node reachable from your start node by a unique path in a cartesian product with every :Node).

Instead, go step by step, collect the distinct nodes (because otherwise you'll get multiples of the same nodes that can be reached via different paths), and then only after you have your collection should you start your match for nodes that aren't in the list.

MATCH (:Node {id:"123"})-[*0..]-(b:Node)
WITH collect(DISTINCT b) as col
MATCH (a:Node)
WHERE NOT a IN col
RETURN a.id