THREE-DIMENSIONAL APOLLONIAN NETWORKS

Danyel J. B. Soares, José S. Andrade, Hans J. Herrmann and LUCIANO R. da Silva
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Danyel J. B. Soares: Departmento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, Campus Universitrio 59072-970, Natal, RN, Brazil
José S. Andrade: Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil
Hans J. Herrmann: Rechnergestützte Physik de Werkstoffe IfB, ETH Zürich, HIF E12, Schafmattstrasse, CH-8093, Zurich
LUCIANO R. da Silva: Departamento de Física, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, Rio Grande do Norte, Brazil

International Journal of Modern Physics C (IJMPC), 2006, vol. 17, issue 08, 1219-1226

Abstract: We discuss the three-dimensional Apollonian network introduced by Andradeet al.1for the two-dimensional case. These networks are simultaneously scale-free, small world, Euclidean, space-filling and matching graphs and have a wide range of applications going from the description of force chains in polydisperse granular packings to the geometry of fully fragmented porous media. Some of the properties of these networks, namely, the connectivity exponent, the clustering coefficient, the shortest path, and vertex betweenness are calculated and found to be particularly rich.

Keywords: Apollonian network; connectivity exponent; clustering coefficient; shortest path; vertex betweenness (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1142/S0129183106009175

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