On certain properties of random apollonian networks

Authors:
Alan Frieze;Charalampos E. Tsourakakis
Affiliations:
Department of Mathematical Sciences, Carnegie Mellon University;Department of Mathematical Sciences, Carnegie Mellon University
Venue:
WAW'12 Proceedings of the 9th international conference on Algorithms and Models for the Web Graph
Year:
2012

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Abstract

In this work we analyze fundamental properties of Random Apollonian Networks [34,35], a popular random graph model which generates planar graphs with power law properties. Specifically, we analyze (a) the degree distribution, (b) the k largest degrees, (c) the k largest eigenvalues and (d) the diameter, where k is a constant.