Graph disjointness is characterized by spectral overlap of Markov transition matrices and tree structures, depending only on vertex and edge sets rather than weights.
Lumpability and marginalisability for continuous-time Markov chains.Journal of Applied Probability, 30(3):518–528, 1993
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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.