I have a question to anyone experienced with graphs and topology. The question is relevant for this topic: https://www.physicsforums.com/threads/a-graph-based-model-of-physics-without-dimensions.887694/ [Broken](adsbygoogle = window.adsbygoogle || []).push({});

Is it possible to construct an arbitrarily large graph (a set of vertices, a set of edges), such that the following is true:

There exists a mapping f(v) of vertices to (x,y,z) coordinates such that

For any pair of vertices m,n:

the euclidean distance of f(m) and f(n) is approximately equal to the length of the shortest path between m and n (inaccuracies are fine so long as the distance is small, but the approximation should be good at larger distances).

In other words, is it possible to construct a graph that effectively simulates a 3 dimensional space?

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# I Constructing dimensions out of a graph structure?

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