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There are many algorithms that address the MST problem, from classical (Boruvka, Prim, Kruskal), optimal (Pettie et al.) to their distributed variants (Bader et al.).

However, I fail to find any references to algorithms that might use spectral properties to algebraically arrive at a suitable representation of the MST (e.g. the set of edges, the adjacency or Laplacian matrix of the MST).

Are there any such algorithms or rationales (proofs) why they don't exist?

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