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

TL;DR

This paper explores space-filling disk packings like Apollonian packings as models for spatial scale-free networks, analyzing their topological and spatial properties and discussing their relevance to energy landscape networks.

Contribution

It introduces the use of self-similar disk packings as models for spatial scale-free networks and characterizes their properties.

Findings

Networks exhibit broad distribution of disk areas.

Topological and spatial properties are systematically characterized.

Potential application as models for energy landscape 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.