Generic saved relationship graphs?

this may be a stupid question with an obvious answer (hope not), but i
haven’t found an answer yet:

is it possible to use a relationship graph query with other tickets,
without having to build it up each time?

i’m asking because we’re trying out scrum and the graphs work really
well for having a high level overview of how things are going for a
particular story. this functionality is a really great addition.

but my VP wants to be able to see it as well without having to manually
build the query for each story’s ticket, so…

it also helps us because our story’s tasks each have a ticket in a queue
respective to its purpose (provisioning, applications, networking,
etc) so the graphs make the cherry picking of tasks way easier.

any input/ideas?