Make a path where next node is not the previous node? - neo4j

Question

I have ~1.5 M nodes in a graph, that are structured like this (picture)
I run a Cypher query that performs calculations on each relationship traversed:
WITH 1 AS startVal
MATCH x = (c:Currency)-[r:Arb*2]->(m)
WITH x, REDUCE(s = startVal, e IN r | s * e.rate) AS endVal, startVal
RETURN EXTRACT(n IN NODES(x) | n) as Exchanges,
extract ( e IN relationships(x) | startVal * e.rate) AS Rel,
endVal, endVal - startVal AS Profit
ORDER BY Profit DESC LIMIT 5
The problem is it returns the path ("One")->("hop")->("One"), which is useless for me.
How can I make it not choose the previously walked node as the next node (i.e. "One"->"hop"->"any_other_node_but_not_"one")?
I have read that NODE_RECENT should address my issue. However, there was no example on how to specify the length of recent nodes in RestAPI or APOC procedures.
Is there a Cypher query for my case?
Thank you.
P.S. I am extremely new (less than 2 month) to Neo4j and coding. So my apologies if there is an obvious simple solution.

Answer 1

I don't know if I understood your question completely, but I believe that you problem can be solved putting a WHERE clause on the MATCH to prevent the not desired relationship be matched, like this:
WITH 1 AS startVal
MATCH x = (c:Currency)-[r:Arb*2]->(m)
WHERE NOT (m)-[:Arb]->(c)
WITH x, REDUCE(s = startVal, e IN r | s * e.rate) AS endVal, startVal
RETURN EXTRACT(n IN NODES(x) | n) as Exchanges,
extract ( e IN relationships(x) | startVal * e.rate) AS Rel,
endVal, endVal - startVal AS Profit
ORDER BY Profit DESC LIMIT 5

Answer 2

Try inserting this clause after your MATCH clause, to filter out cases where c and m are the same:
WHERE c <> m
[EDITED]
That is:
WITH 1 AS startVal
MATCH x = (c:Currency)-[r:Arb*2]->(m)
WHERE c <> m
WITH x, REDUCE(s = startVal, e IN r | s * e.rate) AS endVal, startVal
RETURN EXTRACT(n IN NODES(x) | n) as Exchanges,
extract ( e IN relationships(x) | startVal * e.rate) AS Rel,
endVal, endVal - startVal AS Profit
ORDER BY Profit DESC LIMIT 5;
After using this query to create test data:
CREATE
(c:Currency {name: 'One'})-[:Arb {rate:1}]->(h:Account {name: 'hop'})-[:Arb {rate:2}]->(t:Currency {name: 'Two'}),
(t)-[:Arb {rate:3}]->(h)-[:Arb {rate:4}]->(c)
the above query produces these results:
+-----------------------------------------------------------------------------------------+
| Exchanges | Rel | endVal | Profit |
+-----------------------------------------------------------------------------------------+
| [Node[8]{name:"Two"},Node[7]{name:"hop"},Node[6]{name:"One"}] | [3,4] | 12 | 11 |
| [Node[6]{name:"One"},Node[7]{name:"hop"},Node[8]{name:"Two"}] | [1,2] | 2 | 1 |
+-----------------------------------------------------------------------------------------+