Proximity graphs inside large weighted graphs

Abstract

Given a weighted graph G = (V,E) and a subset U of V, we define several graphs with vertex set U in which two vertices are adjacent if they satisfy a specific proximity rule. These rules use the shortest path distance in G and generalize the proximity rules that generate some of the most common proximity graphs in Euclidean spaces. We prove basic properties of the defined graphs and provide algorithms for their computation. © 2012 Wiley Periodicals, Inc.