Neo4j Cypher path using several times the same edge - neo4j

Question

Let us consider a simple example with two types of nodes: Company and Worker. For any couple of companies c1 and c2 (which respect some conditions that I will ignore here), I'd need to know: 1. How many workers they have in common, how many workers has c1, and how many workers has c2.
My first guess was :
MATCH (w_c1:Worker)--(c1:Company)--(w_common)--(c2:Company)--(w_c2:Worker)
WHERE <something>
RETURN c1, c2, COUNT(DISTINCT w_common), COUNT(DISTINCT w_c1), COUNT(DISTINCT w_c1)
The problem with that request is that, if I have only one link between any pair of connected nodes, COUNT(DISTINCT w_c1) (id for w_c2) does only count the worker of c1 which are not common with c2. But if I have several relations between some nodes, the results is sometimes "correct". It sounds like the path in the match does not "come back" : (w_common)--(c2:Company)--(w_c2:Worker) will no match ("worker1")--("company2")--("worker1") (which may make sense to avoid infinite loops).
My second guess was to split the request in two parts:
My first guess was :
MATCH (c1:Company)--(w_common)--(c2:Company)
MATCH (c1)--(w_c1:Worker), (c2)--(w_c2:Worker)
WHERE <something>
RETURN c1, c2, COUNT(DISTINCT w_common), COUNT(DISTINCT w_c1), COUNT(DISTINCT w_c1)
But then, the results is correct but I have a warning about cartesian products, and indeed, on big dataset, my request does not complete after hours. I tried with a "WITH c1, w_common, c2" between the two matches, but I still have the warning
How should I proceed ?

Answer 1

One thing that will help you is the SIZE() function, which can tell you the number of occurrences of a pattern, such as the number of :Workers per :Company.
This query may work for you, assuming that a Worker working for a Company only has one relationship to that Company:
MATCH (c1:Company)--(w_common:Worker)--(c2:Company)
WHERE <your criteria for matching on a specific c1 and c2>
RETURN COUNT(w_common) as inCommonCount, SIZE( (c1)--(:Worker) ) as c1Count, SIZE( (c2)--(:Worker) ) as c2Count

Answer 2

You can use sub-totals:
OPTIONAL MATCH (C1:Company {name: 'c1'})
OPTIONAL MATCH (C2:Company {name: 'c2'})
WITH C1, C2
MATCH (C:Company)<-[:workto]-(W:Worker) WHERE C = C1 OR C = C2
WITH C1, C2, W,
sum(CASE WHEN C = C1 THEN 1 ELSE 0 END) as tmp1,
sum(CASE WHEN C = C2 THEN 1 ELSE 0 END) as tmp2
RETURN C1, C2,
sum(tmp1) as cc1, sum(tmp2) as cc2,
sum(tmp1 * tmp2 ) as common