Neo4j/Cypher matching first n nodes in the traversal branch

Question

I have graph: (:Sector)<-[:BELONGS_TO]-(:Company)-[:PRODUCE]->(:Product).

I'm looking for the query below.

Start with (:Sector). Then match first 50 companies in that sector and for each company match first 10 products.

First limit is simple. But what about limiting products.

Is it possible with cypher?

UPDATE

As @cybersam suggested below query will return valid results

MATCH (s:Sector)<-[:BELONGS_TO]-(c:Company)
WITH c
LIMIT 50
MATCH (c)-[:PRODUCE]->(p:Product)
WITH c, (COLLECT(p))[0..10] AS products
RETURN c, products

However this solution doesn't scale as it still traverses all products per company. Slice applied after each company products collected. As number of products grows query performance will degrade.

Answer 1

Each returned row of this query will contain: a sector, one of its companies (at most 50 per sector), and a collection of up to 10 products for that company:

MATCH (s:Sector)<-[:BELONGS_TO]-(c:Company)
WITH s, (COLLECT(c))[0..50] AS companies
UNWIND companies AS company
MATCH (company)-[:PRODUCE]->(p:Product)
WITH s, company, (COLLECT(p))[0..10] AS products;

Answer 2

Updating with some solutions using APOC Procedures.

This Neo4j knowledge base article on limiting results per row describes a few different ways to do this.

One way is to use apoc.cypher.run() to execute a limited subquery per row. Applied to the query in question, this would work:

MATCH (s:Sector)<-[:BELONGS_TO]-(c:Company)
WITH c
LIMIT 50
CALL apoc.cypher.run('MATCH (c)-[:PRODUCE]->(p:Product) WITH p LIMIT 10 RETURN collect(p) as products', {c:c}) YIELD value
RETURN c, value.products AS products

The other alternative mentioned is using APOC path expander procedures, providing the label on a termination filter and a limit:

MATCH (s:Sector)<-[:BELONGS_TO]-(c:Company)
WITH c
LIMIT 50
CALL apoc.path.subgraphNodes(c, {maxLevel:1, relationshipFilter:'PRODUCE>', labelFilter:'/Product', limit:10}) YIELD node
RETURN c, collect(node) AS products