Space filling curve for nodes ordering

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I'm trying to convert a set of nodes of a mesh into a space-filling curves.

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Now, I tried both Morton encoding and Hilbert curve, and the Hilber curve was the one which worked best. But I have the following problem:

It could happen that two nodes are neighbours on the curve, but not in the mesh, and this cannot happen in what I need.

Does there exists some other space-filling curve which can preserve this property? Or does anyone have suggestions on how to deal with this?

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