This will give you pairs of actors who have acted together in most number of movies. There are a lot of ties since 7 pairs have acted in 3 movies.
We get the max number of movies the actors acted together (3 movies).
Then again get the pair of actors where they acted in 3 movies.
MATCH (p1:Person)-[:ACTED_IN]->(n:Movie)<-[:ACTED_IN]-(p2:Person) WHERE p1 > p2
WITH p1, p2, count(n) as movies
WITH max(movies) as max_count ORDER by max_count DESC LIMIT 1
MATCH (p1:Person)-[:ACTED_IN]->(n:Movie)<-[:ACTED_IN]-(p2:Person) WHERE p1 > p2
WITH max_count, p1, p2, count(n) as movies where movies = max_count
RETURN p1 as Actor1, p2 as Actor2
It should be easy enough for you to do the other question about;
Which movie has the most number of actors in it?