Effective dimensions and percolation in hierarchically structured scale-free networks

TL;DR

This paper defines and computes dimensions to characterize fractal properties of complex networks, revealing that a hierarchically structured scale-free network is approximately one-dimensional, consistent with percolation and dynamical process results.

Contribution

It introduces new dimension definitions for complex networks and applies them to a specific hierarchically structured scale-free network, revealing its approximate one-dimensionality.

Findings

Network is approximately one-dimensional.

Dimension characterization aligns with percolation results.

Dynamical processes are consistent with the dimensional analysis.

Abstract

We introduce appropriate definitions of dimensions in order to characterize the fractal properties of complex networks. We compute these dimensions in a hierarchically structured network of particular interest. In spite of the nontrivial character of this network that displays scale-free connectivity among other features, it turns out to be approximately one-dimensional. The dimensional characterization is in agreement with the results on statistics of site percolation and other dynamical processes implemented on such a network.