I would say that what I have is a property-directed multi-graph, as I understand it. It's just that the properties are on the edges, and the nodes have no properties except for their ID.
The graph in question is ConceptNet, which in the version I'm working on has about 10 million edges and 3 million nodes. Let's be clear that, in computing, "million" is not a large number. I only said "large graph" to clarify that it's not a small toy graph. The data needs to be imported with some degree of efficiency. But I have a 3TB hard drive and 16 GB of RAM, and both of them can spare a few gigabytes for this task.
Before you throw me into the tarpit of distributed computing, like every other graph-DB provider does as an excuse for their terrible inefficiency, I would like to know if your graph database is appropriate to use with reasonable-sized graphs that fit easily on a single computer.