Some examples for testing traversal in the Gremlin-Cayley dialect.

cayley_example

var movie1 = g.V().Has("name", "The Net")
var movie2 = g.V().Has("name", "Speed")
var actor1 = g.V().Has("name", "Sandra Bullock")
var actor2 = g.V().Has("name", "Keanu Reeves")

////////////////////////////////////

// (film) -> starring -> (actor)
var filmToActor = g.Morphism().Out("/film/film/starring").Out("/film/performance/actor")

// (actor) -> starring -> [film -> starring -> (actor)]
var coStars1 = g.Morphism().In("/film/performance/actor").In("/film/film/starring").Save("name","costar1_movie").Follow(filmToActor)
var coStars2 = g.Morphism().In("/film/performance/actor").In("/film/film/starring").Save("name","costar2_movie").Follow(filmToActor)

// Stars for the movies "The Net" and "Speed"
var m1_actors = movie1.Save("name","movie1").Follow(filmToActor)
var m2_actors = movie2.Save("name","movie2").Follow(filmToActor)

////////////////////////////////////

//Q1: Who starred in both "The Net" and "Speed" ?
//A1: "Sandra Bullock"
//m1_actors.Intersect(m2_actors).Out("name").All()
// Memstore: 7-10ms
// LevelDB: 19-25ms
// Mongo: > 2m (timeout)

//Q2: Did "Keanu Reeves" star in "The Net" ?
//A2: No
//actor2.Intersect(m1_actors).Out("name").All()
// Memstore: 3-7ms
// LevelDB: 7-11ms
// Mongo: 19s

//Q3: Did "Keanu Reeves" star in "Speed" ?
//A3: Yes
//actor2.Intersect(m2_actors).Out("name").All()
// Memstore: 4-7ms
// LevelDB: 8-12ms
// Mongo: 37s

//Q4: Has "Keanu Reeves" co-starred with anyone who starred in "The Net" ?
//A4: "Keanu Reeves" was in "Speed" and "The Lake House" with
//    "Sandra Bullock", who was in "The Net"
actor2.Follow(coStars1).Intersect(m1_actors).Out("name").All()
// Memstore: 101-111ms
// LevelDB: 470-636ms
// Mongo: > 5m (w/ 2m timeout? bug?)

//Q5: Do "Keanu Reeves" and "Sandra Bullock" have any commons co-stars?
//A5: Yes, many. For example: SB starred with "Steve Martin" in "The Prince
//    of Egypt", and KR starred with Steven Martin in "Parenthood".
//actor1.Save("name","costar1_actor").Follow(coStars1).Intersect(
//	actor2.Save("name","costar2_actor").Follow(coStars2)).Out("name").All()
// Memstore: 14.8s
// LevelDB: 1m7s - 1m8s

// Example Q5 result output interpretation:
//    "Sandra Bullock" co-starred with "Steve Martin" in the "Prince of Egypt",
//    and "Keanu Reeves" and "Steve Martin" were both in "Parenthood"
//    
//   "costar1_actor": "Sandra Bullock",
//   "costar1_movie": "The Prince of Egypt",
//   "costar2_actor": "Keanu Reeves",
//   "costar2_movie": "Parenthood",
//   "id": "Steve Martin"

Highly scientific and precise benchmarking method: hitting "Run Query" multiple times, watching the logs on stderr, and throwing out obvious outliers. 15" MBPr, 2.7Ghz i7, 16GB RAM.