One issue in the design of this concept is whether to include the refinement from the IncidenceGraph concepts.

The ability to traverse the vertices of a graph is orthogonal to traversing out-edges, so it would make sense to have a VertexListGraph concept that only includes vertex traversal.

However, such a concept would no longer really be a graph, but would just be a set, and the STL already has concepts for dealing with such things. However, there are many BGL algorithms that need to traverse the vertices and out-edges of a graph, so for convenience a concept is needed that groups these requirements together, hence the VertexListGraph concept.