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## Main Question or Discussion Point

Hello,

I want to prove that a graph represent a manifold, for this i take the opposites edges of a vertex (edge connected between vertex connected to the current vertex) and this subgraph need to be homeomorphic for example to the 1-sphere if i want a 2 manifold. This criterion ensure that my graph represent a manifold.

In 2 dimension its easy (opposite edge homeomorphic to S1) but i have difficulty with higher dimension. Do you know a strategy by using a mathematical approach to prove that ? i think using path based property or homotopy group ? but i am more a physician.

Thanks

Clément Deymier

I want to prove that a graph represent a manifold, for this i take the opposites edges of a vertex (edge connected between vertex connected to the current vertex) and this subgraph need to be homeomorphic for example to the 1-sphere if i want a 2 manifold. This criterion ensure that my graph represent a manifold.

In 2 dimension its easy (opposite edge homeomorphic to S1) but i have difficulty with higher dimension. Do you know a strategy by using a mathematical approach to prove that ? i think using path based property or homotopy group ? but i am more a physician.

Thanks

Clément Deymier