Self-similar disk packings as model spatial scale-free networks

Abstract

The network of contacts in space-filling disk packings, such as the Apollonian packing, are examined. These networks provide an interesting example of spatial scale-free networks, where the topology reflects the broad distribution of disk areas. A wide variety of topological and spatial properties of these systems are characterized. Their potential as models for networks of connected minima on energy landscapes is discussed.

13 pages, 12 figures; some bugs fixed and further discussion of higher-dimensional packings

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