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  • Given a weighted graph G, a natural question to ask is whether there exist another graph H on the same vertex set such that any cut has similar weights in G and H. As the weight of a cut can be described by $\sum_{uv \in E(G)}w_{uv}(x_u-x_v)^2$ where x is a 0-1 vector, one could ask the same question where x can take any real values.
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