Seems like a superset of graphs. On a graph, you only care about what's connected to what. This takes the empty space between into account, as well (fills). I would say it's a separate concept that happens to build on graph theory.
Also isn't it really a segment network? I always think of vectors as having direction and unless I misunderstand, it sounds like this is directionless.
This was my initial reaction too! I wonder how is this different from graphs.
Graphs have a set of vertices and a set of edges, but vector networks also have a set of faces.
Meshes then?
Meshes are closer but vector networks also attach specific attributes to edges which is not usually the case with meshes. Examples: control handles (for curves), stroke weight, dash pattern.
Not uncommon in mesh editors either. Off the top of my head, blender stores edge splits, crease strength, and line styles for the freestyle renderer.