Finding root of a tree in a directed graph - neo4j

Question

I have a tree structure like node(1)->node(2)->node(3). I have name as an property used to retrieve a node.
Given a node say node(3), i wanna retrieve node(1).
Query tried :
MATCH (p:Node)-[:HAS*]->(c:Node) WHERE c.name = "node 3" RETURN p LIMIT 5
But, not able to get node 1.

Answer 1

Your query will not only return "node 1", but it should at least include one path containing it. It's possible to filter the paths to only get the one traversing all the way to the root, however:
MATCH (c:Node {name: "node 3"})<-[:HAS*0..]-(p:Node)
// The root does not have any incoming relationship
WHERE NOT (p)<-[:HAS]-()
RETURN p
Note the use of the 0 length, which matches all cases, including the one where the start node is the root.
Fun fact: even if you have an index on Node:name, it won't be used (unless you're using Neo4j 3.1, where it seems to be fixed since 3.1 Beta2 at least) and you have to explicitly specify it.
MATCH (c:Node {name: "node 3"})<-[:HAS*0..]-(p:Node)
USING INDEX c:Node(name)
WHERE NOT (p)<-[:HAS]-()
RETURN p
Using PROFILE on the first query (with a numerical id property instead of name):
+-----------------------+----------------+------+---------+-------------------------+----------------------+
| Operator | Estimated Rows | Rows | DB Hits | Variables | Other |
+-----------------------+----------------+------+---------+-------------------------+----------------------+
| +ProduceResults | 0 | 1 | 0 | p | p |
| | +----------------+------+---------+-------------------------+----------------------+
| +AntiSemiApply | 0 | 1 | 0 | anon[23], c -- p | |
| |\ +----------------+------+---------+-------------------------+----------------------+
| | +Expand(All) | 1 | 0 | 3 | anon[58], anon[67] -- p | (p)<-[:HAS]-() |
| | | +----------------+------+---------+-------------------------+----------------------+
| | +Argument | 1 | 3 | 0 | p | |
| | +----------------+------+---------+-------------------------+----------------------+
| +Filter | 1 | 3 | 3 | anon[23], c, p | p:Node |
| | +----------------+------+---------+-------------------------+----------------------+
| +VarLengthExpand(All) | 1 | 3 | 5 | anon[23], p -- c | (c)<-[:HAS*]-(p) |
| | +----------------+------+---------+-------------------------+----------------------+
| +Filter | 1 | 1 | 3 | c | c.id == { AUTOINT0} |
| | +----------------+------+---------+-------------------------+----------------------+
| +NodeByLabelScan | 3 | 3 | 4 | c | :Node |
+-----------------------+----------------+------+---------+-------------------------+----------------------+
Total database accesses: 18
and on the second one:
+-----------------------+----------------+------+---------+-------------------------+------------------+
| Operator | Estimated Rows | Rows | DB Hits | Variables | Other |
+-----------------------+----------------+------+---------+-------------------------+------------------+
| +ProduceResults | 0 | 1 | 0 | p | p |
| | +----------------+------+---------+-------------------------+------------------+
| +AntiSemiApply | 0 | 1 | 0 | anon[23], c -- p | |
| |\ +----------------+------+---------+-------------------------+------------------+
| | +Expand(All) | 1 | 0 | 3 | anon[81], anon[90] -- p | (p)<-[:HAS]-() |
| | | +----------------+------+---------+-------------------------+------------------+
| | +Argument | 1 | 3 | 0 | p | |
| | +----------------+------+---------+-------------------------+------------------+
| +Filter | 1 | 3 | 3 | anon[23], c, p | p:Node |
| | +----------------+------+---------+-------------------------+------------------+
| +VarLengthExpand(All) | 1 | 3 | 5 | anon[23], p -- c | (c)<-[:HAS*]-(p) |
| | +----------------+------+---------+-------------------------+------------------+
| +NodeUniqueIndexSeek | 1 | 1 | 2 | c | :Node(id) |
+-----------------------+----------------+------+---------+-------------------------+------------------+
Total database accesses: 13