For every undirected graph G, with nodes $a_1,...,a_n$. Can we find n circles/rings of fixed radius, $c_1,...,c_n$ in 3 dimensions such that there exists an edge between $a_i$ and $a_j$ if and only if $c_i$ and $c_j$ are linked.
This is a simpler version of this question How many ways can n identical rings be interconnected (in 3 dimensions)? In the discussion it quickly became clear that with the ability to make knots and things like the mobius strip makes the problem too difficult. A complete graph is doable by Villarceau circles.