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Can you consider a directed graph the discretization of a 2-manifold equipped with a vector field?

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Isn't a graph a 1-dimensional structure? Or don't you want to discretize the 2-dimensional information of your 2-manifold? –  martini Oct 22 '12 at 7:13
    
I'm sort of thinking of it in the reverse direction- I don't know what the opposite of discretization is. I guess analogous to a graph embedding. –  h8u80iug Oct 22 '12 at 7:20
    
For what purpose? (And what is the vector field? I don't see a distinguished choice of direction to flow at a particular vertex.) –  Qiaochu Yuan Oct 22 '12 at 12:39

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