# Purely spectral algorithms for the minimum spanning tree problem

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?