Speeding up a a query with allShorthestPaths

[Alx]

I have the following cypher query:

MATCH (n:User{id:'id'}) - [:HAS_FAX_NUMBER] -> () <-[:HAS_FAX_NUMBER]-(m1) MATCH p = allShortestPaths((n)-[*]-(m1))
RETURN m1.fhid AS SuggestedUser, COUNT(*) as Connections
UNION
MATCH (n:User{id:'id'}) - [:HAS_PHONE_NUMBER] ->() < - [:HAS_PHONE_NUMBER] -(m2) MATCH p = allShortestPaths((n)-[*]-(m2))
RETURN m2.fhid AS SuggestedUser, COUNT(*) as Connection

This query is quite slow: 3 mins. Is there a way to speed this up? I am basically try to find the how connected is the user in question with m1 or m2. There might be another approach to this. Any ideas or suggestions? Thanks in advance!

[Alx]

I rewrote the query by changing the depth to 2 as follows. I am getting a slight speed-up but not significant. I would appreciate any ideas. 

MATCH (n:User{id:'id'}) - [:HAS_FAX_NUMBER] -> () <-[:HAS_FAX_NUMBER]-(m1) MATCH p = allShortestPaths((n)-[*..2]-(m1))
RETURN m1.fhid AS SuggestedUser, COUNT(p) as Connections
UNION
MATCH (n:User{id:'id'}) - [:HAS_PHONE_NUMBER] ->() < - [:HAS_PHONE_NUMBER] -(m2) MATCH p = allShortestPaths((n)-[*..2]-(m2))
RETURN m2.fhid AS SuggestedUser, COUNT(p) as Connection

[Michael Hunger]

MATCH (n:User{id:'id'}) - [:HAS_FAX_NUMBER] -> () <-[:HAS_FAX_NUMBER]-(m1)

WITH distinct n,m1

MATCH p = allShortestPaths((n)-[*..2]-(m1))
RETURN m1.fhid AS SuggestedUser, COUNT(p) as Connections
UNION
MATCH (n:User{id:'id'}) - [:HAS_PHONE_NUMBER] ->() < - [:HAS_PHONE_NUMBER] -(m2)

WITH distinct n,m2

MATCH p = allShortestPaths((n)-[*..2]-(m2))
RETURN m2.fhid AS SuggestedUser, COUNT(p) as Connection

Michael

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