Finding all steps in property path

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While there are some limitations in what property paths can do, depending on your exact requirements, you may be able to get what you need here. Consider this data:

@prefix : <urn:ex:>.

:a :relatedTo :b .
:b :relatedTo :c .
:c :relatedTo :d .

:a :relatedTo :e .
:e :relatedTo :f .
:f :relatedTo :g .

:h :relatedTo :i .
:i :relatedTo :j .
:j :relatedTo :k .
:k :relatedTo :l .

in which there are three :relatedTo paths:

a --> b --> c --> d
a --> e --> f --> g
h --> i --> j --> k --> l

I realize that in your case, you had a specific subject, but we can generalize a little bit, and ask for each edge in each of these paths with a query like this: 

prefix : <urn:ex:>
select * where {
  # start a path
  ?begin :relatedTo* ?midI .
  FILTER NOT EXISTS { [] :relatedTo ?begin }

  # grab next edge
  ?midI :relatedTo ?midJ .

  # get to the end of the path.
  ?midJ :relatedTo* ?end .
  FILTER NOT EXISTS { ?end :relatedTo [] }
}
order by ?start ?end


$ arq --data data.n3 --query query.sparql
-----------------------------
| begin | midI | midJ | end |
=============================
| :a    | :a   | :b   | :d  |
| :a    | :b   | :c   | :d  |
| :a    | :c   | :d   | :d  |
| :a    | :a   | :e   | :g  |
| :a    | :e   | :f   | :g  |
| :a    | :f   | :g   | :g  |
| :h    | :h   | :i   | :l  |
| :h    | :i   | :j   | :l  |
| :h    | :j   | :k   | :l  |
| :h    | :k   | :l   | :l  |
-----------------------------

which shows each edge of each :relatedTo path. You could make the output a little bit prettier, too:

prefix : <urn:ex:>
select (concat(str(?begin),"--",str(?end)) as ?path) ?midI ?midJ where {
  # start a path
  ?begin :relatedTo* ?midI .
  FILTER NOT EXISTS { [] :relatedTo ?begin }

  # grab next edge
  ?midI :relatedTo ?midJ .

  # get to the end of the path.
  ?midJ :relatedTo* ?end .
  FILTER NOT EXISTS { ?end :relatedTo [] }
}
order by ?path


$ arq --data data.n3 --query query.sparql
--------------------------------------
| path                 | midI | midJ |
======================================
| "urn:ex:a--urn:ex:d" | :a   | :b   |
| "urn:ex:a--urn:ex:d" | :b   | :c   |
| "urn:ex:a--urn:ex:d" | :c   | :d   |
| "urn:ex:a--urn:ex:g" | :a   | :e   |
| "urn:ex:a--urn:ex:g" | :e   | :f   |
| "urn:ex:a--urn:ex:g" | :f   | :g   |
| "urn:ex:h--urn:ex:l" | :h   | :i   |
| "urn:ex:h--urn:ex:l" | :i   | :j   |
| "urn:ex:h--urn:ex:l" | :j   | :k   |
| "urn:ex:h--urn:ex:l" | :k   | :l   |
--------------------------------------

This same approach would let you do some interesting things like finding out how far separated certain nodes are:

prefix : <urn:ex:>
select ?begin ?end (count(*) as ?length) where {
  # start a path
  ?begin :relatedTo* ?midI .
  FILTER NOT EXISTS { [] :relatedTo ?begin }

  # grab next edge
  ?midI :relatedTo ?midJ .

  # get to the end of the path.
  ?midJ :relatedTo* ?end .
  FILTER NOT EXISTS { ?end :relatedTo [] }
}
group by ?begin ?end 


------------------------
| begin | end | length |
========================
| :a    | :g  | 3      |
| :a    | :d  | 3      |
| :h    | :l  | 4      |
------------------------

In the data I provided above, the paths happen to be in alphabetical order and so the sorting produces the edges in the right order. However, even if the edge nodes aren’t in alphabetical, we can still print them in order by computing their position in the list. This query:

prefix : <urn:ex:>
select ?begin ?midI ?midJ (count(?counter) as ?position) ?end where {
  ?begin :relatedTo* ?counter .
  ?counter :relatedTo* ?midI .
  FILTER NOT EXISTS { [] :relatedTo ?begin }

  ?midI :relatedTo ?midJ .

  ?midJ :relatedTo* ?end .
  FILTER NOT EXISTS { ?end :relatedTo [] }
}
group by ?begin ?end ?midI ?midJ 


----------------------------------
| begin | midI | midJ | .1 | end |
==================================
| :a    | :a   | :b   | 1  | :d  |
| :a    | :b   | :c   | 2  | :d  |
| :a    | :c   | :d   | 3  | :d  |
| :a    | :a   | :e   | 1  | :g  |
| :a    | :e   | :f   | 2  | :g  |
| :a    | :f   | :g   | 3  | :g  |
| :h    | :h   | :i   | 1  | :l  |
| :h    | :i   | :j   | 2  | :l  |
| :h    | :j   | :k   | 3  | :l  |
| :h    | :k   | :l   | 4  | :l  |
----------------------------------

We don’t necessary need to see that count, but you could, instead of selecting the position, you could use it as a sorting condition:

prefix : <urn:ex:>
select ?begin ?midI ?midJ ?end
 where {
  ?begin :relatedTo* ?counter .
  ?counter :relatedTo* ?midI .
  FILTER NOT EXISTS { [] :relatedTo ?begin }

  ?midI :relatedTo ?midJ .

  ?midJ :relatedTo* ?end .
  FILTER NOT EXISTS { ?end :relatedTo [] }
}
group by ?begin ?end ?midI ?midJ 
order by ?begin ?end count(?counter)

and be guaranteed to get your edges in sequence.

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