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I think this has gotten me closer to a solution, but I'm running into a compile issue:
...
where line 136 is:
pe.edge_id = get_edge_id(graph_t, pe.parent_id, pe.vertex_id);
graph_t is a type not an object.
also, get_edge_id will require template parameters, how about:
pe.edge_id = get_edge_id
Also it occurs to me that getting the edge based on the vertexes rather than the vertex ids might be faster.
It will be just the same. Since the vertices are stored in a vector, vertex_descriptors are just indices to a vector.