Github user spmallette commented on the pull request:
https://github.com/apache/tinkerpop/commit/e790e56aaa2118b07e36f2579502786bd9d79cc0#commitcomment-17841823
In docs/src/recipes/centrality.asciidoc:
In docs/src/recipes/centrality.asciidoc on line 75:
> Note that I had to remove the sack normalization as it seems to be buggy
for this query
I don't see that behavior actually - see the results below (first with
modern graph and then with my example graph from the recipe.
```text
gremlin> g.withSack(0).V().repeat(both().simplePath()).emit().path().
gremlin> group().by(project("a","b").by(limit(local, 1)).
gremlin> by(tail(local, 1))).
gremlin> by(order().by(count(local))).
gremlin> select(values).as("shortestPaths").
gremlin> V().as("v").map(select("shortestPaths").unfold().
gremlin> filter(unfold().where(eq("v"))).count()).
gremlin> sack(sum).barrier(normSack).sack().as("betweeness").
gremlin> select("v","betweeness")
==>[v:v[1], betweeness:0.21428571428571427]
==>[v:v[2], betweeness:0.11904761904761904]
==>[v:v[3], betweeness:0.21428571428571427]
==>[v:v[4], betweeness:0.21428571428571427]
==>[v:v[5], betweeness:0.11904761904761904]
==>[v:v[6], betweeness:0.11904761904761904]
gremlin>
gremlin>
g.withSack(0).V().store("x").repeat(both().simplePath()).emit().path().
gremlin> group().by(project("a","b").by(limit(local, 1)).
gremlin> by(tail(local, 1))).
gremlin> by(order().by(count(local))).
gremlin> select(values).as("shortestPaths").
gremlin> select("x").unfold().as("v").
gremlin> select("shortestPaths").
gremlin> map(unfold().filter(unfold().where(eq("v"))).count()).
gremlin> sack(sum).barrier(normSack).sack().as("betweeness").
gremlin> select("v","betweeness")
==>[v:v[1], betweeness:0.21428571428571427]
==>[v:v[2], betweeness:0.11904761904761904]
==>[v:v[3], betweeness:0.21428571428571427]
==>[v:v[4], betweeness:0.21428571428571427]
==>[v:v[5], betweeness:0.11904761904761904]
==>[v:v[6], betweeness:0.11904761904761904]
gremlin> graph = TinkerGraph.open()
==>tinkergraph[vertices:0 edges:0]
gremlin> g = graph.traversal()
==>graphtraversalsource[tinkergraph[vertices:0 edges:0], standard]
gremlin> a = graph.addVertex('name','a')
==>v[0]
gremlin> b = graph.addVertex('name','b')
==>v[2]
gremlin> c = graph.addVertex('name','c')
==>v[4]
gremlin> d = graph.addVertex('name','d')
==>v[6]
gremlin> e = graph.addVertex('name','e')
==>v[8]
gremlin> a.addEdge('next',b)
==>e[10][0-next->2]
gremlin> b.addEdge('next',c)
==>e[11][2-next->4]
gremlin> c.addEdge('next',d)
==>e[12][4-next->6]
gremlin> d.addEdge('next',e)
==>e[13][6-next->8]
gremlin> g.withSack(0).V().repeat(both().simplePath()).emit().path().
gremlin> group().by(project("a","b").by(limit(local, 1)).
gremlin> by(tail(local, 1))).
gremlin> by(order().by(count(local))).
gremlin> select(values).as("shortestPaths").
gremlin> V().as("v").map(select("shortestPaths").unfold().
gremlin> filter(unfold().where(eq("v"))).count()).
gremlin> sack(sum).barrier(normSack).sack().as("betweeness").
gremlin> select("v","betweeness")
==>[v:v[0], betweeness:0.13333333333333333]
==>[v:v[2], betweeness:0.23333333333333334]
==>[v:v[4], betweeness:0.26666666666666666]
==>[v:v[6], betweeness:0.23333333333333334]
==>[v:v[8], betweeness:0.13333333333333333]
gremlin>
gremlin>
g.withSack(0).V().store("x").repeat(both().simplePath()).emit().path().
gremlin> group().by(project("a","b").by(limit(local, 1)).
gremlin> by(tail(local, 1))).
gremlin> by(order().by(count(local))).
gremlin> select(values).as("shortestPaths").
gremlin> select("x").unfold().as("v").
gremlin> select("shortestPaths").
gremlin> map(unfold().filter(unfold().where(eq("v"))).count()).
gremlin> sack(sum).barrier(normSack).sack().as("betweeness").
gremlin> select("v","betweeness")
==>[v:v[0], betweeness:0.13333333333333333]
==>[v:v[2], betweeness:0.23333333333333334]
==>[v:v[4], betweeness:0.26666666666666666]
==>[v:v[6], betweeness:0.23333333333333334]
==>[v:v[8], betweeness:0.13333333333333333]
```
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