Proximity graphs inside large weighted graphs

Authors:
Bernardo M. Ábrego;Ruy Fabila-Monroy;Silvia Fernández-Merchant;David Flores-Peñaloza;Ferran Hurtado;Henk Meijer;Vera Sacristán;Maria Saumell
Affiliations:
Department of Mathematics, California State University, Northridge, California;Departamento de Matemáticas, CINVESTAV, Mexico DF, Mexico;Department of Mathematics, California State University, Northridge, California;Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico;Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Barcelona, Spain;Science Department, Roosevelt Academy, Middelburg, The Netherlands;Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Barcelona, Spain;Department of Applied Mathematics, Charles University, Prague, Czech Republic
Venue:
Networks
Year:
2013

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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. NETWORKS, 2013 © 2013 Wiley Periodicals, Inc.