Probabilistic embedding of discrete sets as continuous metric spaces

Ph Blanchard, D. Volchenkov

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Any symmetric affinity function w: V × V → ℝ+ defined on a discrete set V induces Euclidean space structure on V. In particular, an undirected graph specified by an affinity (or adjacency) matrix can be considered as a metric topological space. We have calculated the visual representations of the probabilistic locus for a chain, a polyhedron and a finite 2D lattice.

Original languageEnglish
Pages (from-to)259-268
Number of pages10
Issue number3-4
StatePublished - 2009


  • Euclidean space
  • Probabilistic analogue
  • Random walk


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