Abstract
We discuss the three-dimensional Apollonian network introduced by
Andrade et al.(1) for 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.
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