Very slow this cypher query, is there any optimization? - neo4j

Question

Using Neo4J 2.1.5.
Data:
2000 persons
Goal: For each person, calculate the total of friends, friends' friends, friends' friends' friends.
Result is like follows:
Person FullName | Friends total | Friends-2 total | Friends-3 total | global total
MATCH (person:Person)
WITH person
OPTIONAL MATCH person-[:KNOWS]-(p2:Person)
WITH person, count(p2) as f1
OPTIONAL MATCH path = shortestPath(person-[:KNOWS*..2]-(f2:Person))
WHERE length(path) = 2
WITH count(nodes(path)[-1]) AS f2, person, f1
OPTIONAL MATCH path = shortestPath(person-[:KNOWS*..3]-(f3:Person))
WHERE length(path) = 3
WITH count(nodes(path)[-1]) AS f3, person, f2, f1
RETURN person._firstName + " " + person._lastName, f1, f2, f3, f1+f2+f3 AS total
The tricks is to avoid wrong calculations with cylic graph; that's why I use shortestPath.
However, this query lasts long: 60 seconds!
Any optimization possible?

Answer 1

[EDITED]
Does this work for you?
MATCH (person:Person)
OPTIONAL MATCH (person)-[:KNOWS]-(p1:Person)
WITH person, COALESCE(COLLECT(p1),[]) AS p1s
WITH person, CASE p1s WHEN [] THEN [NULL] ELSE p1s END AS p1s
UNWIND p1s AS p1
OPTIONAL MATCH (p1)-[:KNOWS]-(p2:Person)
WHERE NOT ((p2 = person) OR (p2 IN p1s))
WITH person, p1s, COALESCE(COLLECT(DISTINCT p2),[]) AS p2s
WITH person, p1s, CASE p2s WHEN [] THEN [NULL] ELSE p2s END AS p2s UNWIND p2s AS p2
OPTIONAL MATCH (p2)-[:KNOWS]-(p3:Person)
WHERE NOT ((p3 = person) OR (p3 IN p1s) OR (p3 IN p2s))
WITH person,
CASE p1s WHEN [NULL] THEN 0 ELSE SIZE(p1s) END AS f1,
CASE p2s WHEN [NULL] THEN 0 ELSE SIZE(p2s) END AS f2,
COUNT(DISTINCT p3) AS f3
RETURN person.firstName + " " + person.lastName, f1, f2, f3, f1+f2+f3 AS total;
Each friend is only counted once.
Here is an explanation of some of the more obscure tactics used. The query has to to replace empty p1s and p2s collections with [NULL] so that UNWIND will not abort the rest of the query. Then, when counting the size of the collections, we need give [NULL] collections a count of 0.