Neo4j: match with multiple relations in timely manner - graph

Question

Consider following nodes that are connected between each other with 2 type of edges: direct and intersect. The query needs to discover all possible paths between 2 nodes that satisfies all following rules:
0..N direct edges
0..1 intersect edge
intersect edge can be between direct edges
These paths are considered valid between nodeA and nodeZ:
(nodeA)-[:direct]->(nodeB)-[:direct]->(nodeC)->[:direct]->(nodeZ)
(nodeA)-[:intersect]->(nodeB)-[:direct]->(nodeC)->[:direct]->(nodeZ)
(nodeA)-[:direct]->(nodeB)-[:intersect]->(nodeC)->[:direct]->(nodeZ)
(nodeA)-[:direct]->(nodeB)->[:direct]->(nodeC)-[:intersect]->(nodeZ)
Basically intersect edge can happen anywhere in the path but only once.
My ideal cypher query in non-existing neo4j version would be this:
MATCH (from)-[:direct*0..N|:intersect*0..1]->(to)
But neo4j doesn't support multiple constraints for edges type :(.
UPDATE 23.04.16
There 6609 nodes (out of 550k total), 5184 edges of type direct (out of 440k total) and 34119 of type intersect (out of 37289 total). There are some circular references expected (which neo4j avoids, isn't it?)
The query that looked promising but failed to finish in a manner of seconds:
MATCH p = (from {from: 1})-[:direct|intersect*0..]->(to {to: 99})
WHERE
123 < from.departureTS < 123 + 86400 //next day
AND REDUCE(s = 0, x IN RELATIONSHIPS(p) | CASE TYPE(x) WHEN 'intersect' THEN s + 1 ELSE s END) <= 1
return p;

Answer 1

Here is a query that conforms to the stated requirements:
MATCH p = (from)-[:direct|intersect*0..]->(to)
WHERE REDUCE(s = 0, x IN RELATIONSHIPS(p) |
CASE WHEN TYPE(x) = 'intersect' THEN s + 1 ELSE s END) <= 1
return p;
It returns all paths with 0 or more direct relationships and 0 or 1 intersect relationships.

Answer 2

This will do what you want:
// Cybersam's correction:
MATCH p = ((from)-[:direct*0..]->(middle)-[:intersect*0..1]->(middle2)-[:direct*0..]->(to)‌​) return DISTINCT p;
return p
Here's the test scenario I used:
create (a:nodeA {name: "A"})
create (b:nodeB {name: "B"})
create (c:nodeC {name: "C"})
create (z:nodeZ {name: "Z"})
merge (a)-[:direct {name: "D11"}]->(b)-[:direct {name: "D21"}]->(c)-[:direct {name: "D31"}]->(z)
merge (a)-[:intersect {name: "I12"}]->(b)-[:direct {name: "D22"}]->(c)-[:direct {name: "D32"}]->(z)
merge (a)-[:direct {name: "D13"}]->(b)-[:intersect {name: "I23"}]->(c)-[:direct {name: "D33"}]->(z)
merge (a)-[:direct {name: "D14"}]->(b)-[:direct {name: "D24"}]->(c)-[:intersect {name: "I34"}]->(z)
merge (a)-[:intersect {name: "I15"}]->(z)
// Cybersam's correction:
MATCH p = ((from)-[:direct*0..]->(middle)-[:intersect*0..1]->(middle2)-[:direct*0..]->(to)‌​) return DISTINCT p;
return p
I made the mistake of thinking the graph on the browser reflected the data that was returned in "p" - it did not, you have to look at the "rows" part of the report to get all the details.
This query will also return single nodes- which fits the requirements.