Skeleton and fractal scaling in complex networks

TL;DR

This paper explores how fractal scaling in certain complex networks stems from an underlying tree structure called the skeleton, which is based on edge betweenness centrality, and introduces a model capturing these properties.

Contribution

It reveals the origin of fractal scaling in networks as stemming from a fractal skeleton with critical branching properties and introduces a model combining fractal scaling and scale-invariance.

Findings

Fractal networks are rooted in a skeleton with critical branching properties.

The original networks can be viewed as skeletons with local shortcuts.

A new in-silico model reproduces fractal scaling and scale-invariance.

Abstract

We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the property of the critical branching tree. The original fractal networks are viewed as a fractal skeleton dressed with local shortcuts. An in-silico model with both the fractal scaling and the scale-invariance properties is also constructed. The framework of fractal networks is useful in understanding the utility and the redundancy in networked systems.