Graph disjointness is characterized by spectral overlap of Markov transition matrices and tree structures, depending only on vertex and edge sets rather than weights.
Analysis of a nonreversible Markov chain sampler.Annals of Applied Probability, pages 726–752, 2000
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Graph Disjointness with Applications to Reversible Markov Chains
Graph disjointness is characterized by spectral overlap of Markov transition matrices and tree structures, depending only on vertex and edge sets rather than weights.