I am not so fond of typedefs. Instead I propose to use the using-syntax:
using vertex_descriptor = int;
Furthermore we can inline your traversal_category by using nameless structs (I think you would never really do this in production code, but it's nice to see a reasonable application of this strange feature): ideone.com/9ObFoG
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Furthermore we can inline your traversal_category by using nameless structs (I think you would never really do this in production code, but it's nice to see a reasonable application of this strange feature):
ideone.com/9ObFoG