Iso-Graph: Its Definition and Properties

Abstract This paper introduces a discrete Reeb graph model, called iso-graph, on arbitrary graphs, and discusses its properties. We define a sect on a graph as an edge subset which, if removed, transects the input graph, changing it homotopically. We show that an iso-graph is essentially a collection of sects which are nested and not inversely tangent. The iso-graph model can be used as a substitute for existing discrete Reeb graphs with the advantages of avoiding data perturbation and interpolation.