A Note on Diffusion State Distance

TL;DR

This paper extends the understanding of diffusion state distance (DSD) by proving its convergence for general finite irreducible Markov chains, broadening its applicability beyond symmetric or reversible cases.

Contribution

It demonstrates that DSD converges under more general conditions using classical potential theory, unlike previous results limited to symmetric or reversible walks.

Findings

DSD converges for general finite irreducible Markov chains

Classical potential theory underpins the convergence proof

Broader applicability of DSD in graph analysis

Abstract

Diffusion state distance (DSD) is a metric on the vertices of a graph, motivated by bioinformatic modeling. Previous results on the convergence of DSD to a limiting metric relied on the definition being based on symmetric or reversible random walk on the graph. We show that convergence holds even when the DSD is based on general finite irreducible Markov chains. The proofs rely on classical potential theory of Kemeny and Snell.