Energy landscapes, scale-free networks and Apollonian packings

TL;DR

This paper reviews the topological properties of two types of spatial scale-free networks, linking their similarities to the fractal nature of energy landscapes and basin packings, providing insights into their scale-free characteristics.

Contribution

It proposes that the energy landscape's fractal basin packing explains the scale-free topology of inherent structure networks and compares two specific network types.

Findings

Inherent structure and Apollonian networks share topological features.

The energy landscape can be modeled as a fractal packing of basins.

These properties elucidate the scale-free nature of the networks.

Abstract

We review recent results on the topological properties of two spatial scale-free networks, the inherent structure and Apollonian networks. The similarities between these two types of network suggest an explanation for the scale-free character of the inherent structure networks. Namely, that the energy landscape can be viewed as a fractal packing of basins of attraction.