Sometimes you just need someone to question your logic to help you. I have been thinking about the solution for days. Thank you Cobra.
Here is the query I need (in case anyone needs it):
MATCH (n1:Node{uuid: "n1_34"}) -- (n2:Node)
MATCH (n1) -- () -[r]- (n2) RETURN n2.uuid AS uuid, count(r) AS n
ORDER BY n DESC
I will surely take a look at the article if I need to project a subgraph. Thanks again.