Yes, of course you could always select a node (often you'd always have to start from a single root node), select arcs, filter the arcs by some criteria, etc.
But I've never seen a complex query language that would allow to express any complex traversal strategies (like Dijkstra algorithm), and from your wording I concluded that this was your requirement for something to be called a graph database.
Query language isn't a requirement but exposing the capability to do those kinds of selects / filtering operations is. It doesn't have to support Dijkstra's algorithm but it should be possible to implement it (efficiently).
I'd encourage you to look at the product and see whether it meets your definition.