Neo4j shortestPath with highest aggregated relationship propertie - neo4j

Question

I want to find the shortest path between two nodes. The path itself is not the problem... The bigger problem is, that I´ll want to return the path, where the aggregated relationship property on the path is highest.
For better understanding, here´s what I want:
This is my query
MATCH
(startNode:Person {id:"887111"}),
(endNode:Person {id:"789321"}),
paths = allShortestPaths((startNode)-[r:KNOWS *..20]-(endNode))
RETURN paths
In this example I´ll want to have the path from Elissa (id: 887111) to Kasey (id: 789321) where the aggregated count ON the relationship is MAX.
I´ve also had a look at 'shortestPath', which only gives me one path. The other way is to call the 'dijkstra'-algo, with this I´ll get only the path with the lowest 'cost' (and not the highest).
So in my example the only path which should shown up is Elissa->Travon->Kasey
I´d think, the problem isn´t that complex, but at the moment I´m gettin stucked with this..
Thanks so far in advance.
UPDATE
after calling the suggested query
MATCH (startNode:Person {id:"789321"}), (endNode:Person {id:"887111"})
CALL apoc.algo.dijkstra(startNode, endNode, 'KNOWS', '_duration') YIELD path, weight
RETURN path, -weight AS weight
my result is the following

Answer 1

[UPDATED]
I present 2 answers, depending one what you are trying to do.
1. Finding path with max total weight
To find the path with max total weight, you can feed to the Dijkstra algorithm the negation of the original weight properties. The resulting "lowest" total weight will be a negative value that, when negated, will actually be the highest total weight (based on the original weight properties).
There is an APOC procedure, apoc.algo.dijkstra that implements the Dijkstra algorithm, but it does not allow you to use the negative value of the specified weight property. So, to use that procedure, you would need to add a new property to each KNOWS relationship with the appropriate negative value. For example, to add the negative weights to existing relationships (assuming w is the original weight property, and _w will contain the corresponding negative value):
MATCH ()-[k:KNOWS]->()
SET k._w = -k.w;
Once you have the negative weights, the following should give you the path with the max weight:
MATCH (startNode:Person {id:"887111"}), (endNode:Person {id:"789321"})
CALL apoc.algo.dijkstra(startNode, endNode, 'KNOWS', '_w') YIELD path, weight
RETURN path, -weight AS weight;
2. Choosing from the shortest paths the one with maximum total weight
MATCH
(startNode:Person {id:"887111"}),
(endNode:Person {id:"789321"}),
path = allShortestPaths((startNode)-[:KNOWS *..20]-(endNode))
RETURN path, REDUCE(s = 0, r IN RELATIONSHIPS(path) | s + r.duration) AS weight
ORDER BY weight DESC
LIMIT 1;