http://franz.com/ns/allegrograph/4.11/sna/bidirectionalSearch
Compute Bidirectional Search paths.
This magic property can be used in several ways:
The first is:
?start sna:bidirectionalSearch ( ex:namedGenerator ?end )
 ?start sna:bidirectionalSearch ( ex:namedGenerator ?end ?depth )    which will succeed when there is a path between  ?start  and  ?end  (both of which must be bound) using generator  ex:namedGenerator  and the optional  ?depth  to limit the search. 
The second is
(?start ?node) sna:bidirectionalSearch ( ex:namedGenerator ?end )
 (?start ?node) sna:bidirectionalSearch ( ex:namedGenerator ?end ?depth )    which is like the above but also returns one binding to  ?node  for each node along the path between  ?start  and  ?end . Note that although they will tend to appear in sequence there is no guaranteed order between the bindings. The third form provides a way to capture the order in the path. It is: 
(?start ?node ?nodeId) sna:bidirectionalSearch ( ex:namedGenerator ?end )
 (?start ?node ?nodeId) sna:bidirectionalSearch ( ex:namedGenerator ?end ?depth )    which is like the above but also returns one binding to  ?node  for each node along the path and a sequential numeric binding to  ?nodeId  that represents the path element. 
The final form is:
(?start ?node ?nodeId ?pathId) sna:bidirectionalSearch ( ex:namedGenerator ?end )
 (?start ?node ?nodeId ?pathId) sna:bidirectionalSearch ( ex:namedGenerator ?end ?depth )    It is like the above but also binds  ?pathId  to a sequential count of the number of the path. I.e., the first path will have  ?pathId  bound to 0; the second to 1 and so on. 
Notes
The following namespace abbreviations are used:
- fti - <http://franz.com/ns/allegrograph/2.2/textindex/>
 - geo - <http://franz.com/ns/allegrograph/3.0/geospatial/>
 - geofn - <http://franz.com/ns/allegrograph/3.0/geospatial/fn/>
 - nd - <http://franz.com/ns/allegrograph/5.0/geo/nd#>
 - ndfn - <http://franz.com/ns/allegrograph/5.0/geo/nd/fn#>
 - sna - <http://franz.com/ns/allegrograph/4.11/sna/>
 
The SPARQL magic properties reference has additional information on using AllegroGraph magic properties and functions.