Good way to set relation to an edge in Neo4j - neo4j

Question

For my project I need to create a relation to an edge in Neo4j graph database.
Let's illustrate on example of a flight provider who operates flights from Rome to London (and back) and also from Oslo to Lisbon.
CREATE (l:City{name:"London"})
(r:City{name:"Rome"}),
(li:City{name:"Lisbon"})
(o:City{name:"Oslo"}),
(op:Operator{name:"One"}),
(l)<-[f:FlightRoute{distance:900}]->(r)
How would you link Operator One to London, Rome, Lisbon and Oslo to suggest that this operator connects these cities (l<-->r & li<-->o) but not e.g. r<-->o. Other operators would be doing other cities. So basically I would like to link op to 2 edges.
Queries to perform would be to find all operators doing various lines. Calculating overall distances of operations (assuming <--> has distance parameter) etc.
I can imagine only to create a node between (l) and (r). Is there some other way?

Answer 1

As you suspected, "reification" (i.e., turning a relationship into a node) is probably the best way to handle your situation.
Here is an example of a query that adds the fact that an operator operates a flight from London to Rome:
MATCH (l:City {name:"London"}),
(r:City {name:"Rome"}),
(op:Operator {name:"One"})
CREATE (l)<-[:FROM]-(f:FlightRoute{distance:900})-[:TO]->(r),
(op)-[:OPERATES]->(f);
And a similar query for a flight from Lisbon to Oslo:
MATCH (li:City {name:"Lisbon"}),
(o:City {name:"Oslo"}),
(op:Operator {name:"One"})
CREATE (li)<-[:FROM]-(f:FlightRoute{distance:21})-[:TO]->(o),
(op)-[:OPERATES]->(f);
To find all operators between London and Rome:
MATCH (l:City {name:"London"})<-[:FROM|TO]-(f)-[:FROM|TO]->(r:City {name:"Rome"}),
(op:Operator)-[:OPERATES]->(f)
RETURN DISTINCT op;
To find overall distance for all flights of an operator:
MATCH (op:Operator {name:"One"})-[:OPERATES]->(f)
RETURN SUM(f.distance);
Indexes (or uniqueness constraint) for :City(name) and Operator(name) would help to speed up the above queries.