[naasking]

I'm not clear what an abstraction that makes edges first class but vertices second class looks like. An edge connects two vertices, so if two edges connect to the same vertex, what does this look like?

[dataflow]

The most minimal example of it I can think of would be a little ridiculous, but it could look like this:

  interface Edge { }
  interface Graph {
    List<Edge> getRoots();  // Returns some ~minimal set of edges with connectivity to all the others
    List<Edge> getAdjacentEdges(Edge e, boolean tail);
  }

There's no way to directly refer to a vertex here at all (unlike with edges), and yet (since edges have identity) there's enough information to determine the graph structure!

[naasking]

What's an example of an algorithm that could use this sort of interface? All of the algorithms that immediately come to mind are more require more vertex information.