Neo4j deep hierarchy query - neo4j

Question

I've this kind of data model in the db:
(a)<-[:has_parent]<-(b)-[:has_parent]-(c)<-[:has_parent]-(...)
every parent can have multiple children & this can go on to unknown number of levels.
I want to find these values for every node
the number of descendants it has
the depth [distance from the node] of every descendant
the creation time of every descendant
& I want to rank the returned nodes based on these values. Right now, with no optimization, the query runs very slow (especially when the number of descendants increases).
The Questions:
what can I do in the model to make the query performant (indexing, data structure, ...)
what can I do in the query
what can I do anywhere else?
edit:
the query starts from a specific node using START or MATCH
to clarify:
a. the query may start from any point in the hierarchy, not just the root node
b. every node under the starting node is returned ranked by the total number of descendants it has, the distance (from the returned node) of every descendant & timestamp of every descendant it has.
c. by descendant I mean everything under it, not just it's direct children
for example,
here's a sample graph:
http://console.neo4j.org/r/awk6m2

Answer 1

First you need to know how to find the root node. The following statement finds the nodes having no outboung parent relationship - be aware that statement is potentially expensive in a large graph.
MATCH (n)
WHERE NOT ((n)-[:has_parent]->())
RETURN n
Instead you should use an index to find that node:
MATCH (n:Node {name:'abc'})
Starting with our root node, we traverse inbound parent relationship with variable depth. On each node traversed we calculate the number of children - since this might be zero a OPTIONAL MATCH is used:
MATCH (root:Node) // line 1-3 to find root node, replace by index lookup
WHERE NOT ((root)-[:has_parent]->())
WITH root
MATCH p =(root)<-[:has_parent*]-() // variable path length match
WITH last(nodes(p)) AS currentNode, length(p) AS currentDepth
OPTIONAL MATCH (currentNode)<-[:has_parent]-(c) // tranverse children
RETURN currentNode, currentNode.created, currentDepth, count(c) AS countChildren