Probabilistic embedding of discrete sets as continuous metric spaces

Abstract

Any symmetric affinity function 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.

Keywords:

• Euclidean space
• random walk
• probabilistic analogue

Acknowledgements

This work has been supported by the Volkswagen Foundation (Germany) in the framework of the project ‘Network formation rules, random set graphs and generalized epidemic processes’ (Contract no Az.: I/82 418).