It can be done, but I could not find a simple solution. So let's go with the complicated one.
First, create an example graph:
CREATE
(a:Entity {name: 'a'}),
(b:Entity {name: 'b'}),
(c:Entity {name: 'c'}),
(d:Entity {name: 'd'}),
(e:Entity {name: 'e'}),
(a)-[:REL {name: 'r1'}]->(b)
<-[:REL {name: 'r2'}]-(c)
-[:REL {name: 'r3'}]->(d)
-[:REL {name: 'r4'}]->(e)

Use this query:
MATCH (e1 {name: 'a'})-[rels*1..4]-(e2 {name: 'e'})
WITH e1, e2, rels,
extract(rel IN rels | startNode(rel)) AS startNodes,
extract(rel IN rels | endNode(rel)) AS endNodes,
range(1, size(rels)-1) AS indexes
WITH e1, e2, rels, startNodes, endNodes, indexes, startNodes[0] AS start
UNWIND indexes AS i
WITH e1, e2,
e1 = start as isOutFirst,
(endNodes[i-1] = startNodes[i] OR
startNodes[i-1] = startNodes[i]) AS isOut
WITH e1, e2, isOutFirst, collect(isOut) AS isOuts
RETURN e1, e2, [isOutFirst] + isOuts AS isOuts
The result is:
╒═════════╤═════════╤═════════════════════════╕
│e1 │e2 │isOuts │
╞═════════╪═════════╪═════════════════════════╡
│{name: a}│{name: e}│[true, false, true, true]│
└─────────┴─────────┴─────────────────────────┘
The main ideas are the following:
- We get the start and end node for each relationship using the
extract
method.
- We use the
range
function and UNWIND
to generate a list of indexes and "iterate" on the lists.
- The i. relationship is outgoing (
isOut
) if it starts from any node of the previous (i-1.) relationship.
- The 0. relationship has no previous relationship, hence we treat it separately (
isOutFirst
).
- We collect the
isOut
values to an isOuts
list.
- We combine the
isOutFirst
variable and the isOuts
list to a single list.
You can UNWIND
the results and add the corresponding relationship types:
MATCH (e1 {name: 'a'})-[rels*1..4]-(e2 {name: 'e'})
WITH e1, e2, rels,
extract(rel IN rels | startNode(rel)) AS startNodes,
extract(rel IN rels | endNode(rel)) AS endNodes,
range(1, size(rels)-1) AS indexes
WITH e1, e2, rels, startNodes, endNodes, indexes, startNodes[0] AS start
UNWIND indexes AS i
WITH e1, e2, rels,
e1 = start as isOutFirst,
(endNodes[i-1] = startNodes[i] OR
startNodes[i-1] = startNodes[i]) AS isOut
WITH e1, e2, rels, isOutFirst, collect(isOut) AS isOuts
WITH e1, e2, rels,
[isOutFirst] + isOuts AS isOuts,
range(0, size(rels)-1) AS indexes2
UNWIND indexes2 AS i
RETURN e1, e2, type(rels[i]) AS relType, isOuts[i] AS isOut
This results in:
╒═════════╤═════════╤═══════╤═════╕
│e1 │e2 │relType│isOut│
╞═════════╪═════════╪═══════╪═════╡
│{name: a}│{name: e}│REL │true │
├─────────┼─────────┼───────┼─────┤
│{name: a}│{name: e}│REL │false│
├─────────┼─────────┼───────┼─────┤
│{name: a}│{name: e}│REL │true │
├─────────┼─────────┼───────┼─────┤
│{name: a}│{name: e}│REL │true │
└─────────┴─────────┴───────┴─────┘
Update: you can use the direction to extract the nodes in the correct order from the path:
MATCH (e1 {name: 'a'})-[rels*1..4]-(e2 {name: 'e'})
WITH e1, e2, rels,
extract(rel IN rels | startNode(rel)) AS startNodes,
extract(rel IN rels | endNode(rel)) AS endNodes,
range(1, size(rels)-1) AS indexes
WITH e1, e2, rels, startNodes, endNodes, indexes, startNodes[0] AS start
UNWIND indexes AS i
WITH e1, e2, rels,
e1 = start as isOutFirst,
(endNodes[i-1] = startNodes[i] OR
startNodes[i-1] = startNodes[i]) AS isOut
WITH e1, e2, rels, isOutFirst, collect(isOut) AS isOuts
WITH e1, e2, rels,
[isOutFirst] + isOuts AS isOuts,
range(0, size(rels)-1) AS indexes2
UNWIND indexes2 AS i
RETURN e1, e2, type(rels[i]) AS relType,
CASE isOuts[i]
WHEN true THEN startNode(rels[i])
ELSE endNode(rels[i])
END AS node1,
CASE isOuts[i]
WHEN true THEN endNode(rels[i])
ELSE startNode(rels[i])
END AS node2
This results in:
╒═════════╤═════════╤═══════╤═════════╤═════════╕
│e1 │e2 │relType│node1 │node2 │
╞═════════╪═════════╪═══════╪═════════╪═════════╡
│{name: a}│{name: e}│REL │{name: a}│{name: b}│
├─────────┼─────────┼───────┼─────────┼─────────┤
│{name: a}│{name: e}│REL │{name: b}│{name: c}│
├─────────┼─────────┼───────┼─────────┼─────────┤
│{name: a}│{name: e}│REL │{name: c}│{name: d}│
├─────────┼─────────┼───────┼─────────┼─────────┤
│{name: a}│{name: e}│REL │{name: d}│{name: e}│
└─────────┴─────────┴───────┴─────────┴─────────┘
Limitations: the solutions above might not work if there is a 2-length circle in the graph, e.g. for a graph (a)<-[r1]-(b)<-[r2]-(a)
, they incorrectly mark (b)<-[r2]-(a)
as outgoing for one of the paths.