Spectral Scaling in Complex Networks

TL;DR

This paper explores how spectral properties reveal the presence of topological isotropy or anisotropy in complex networks, analyzing real-world systems to understand their structural scaling behaviors.

Contribution

It introduces a spectral method to identify topological isotropy in complex networks and applies it to diverse real-world systems.

Findings

Power-law scaling indicates topological isotropy in some networks.

Spectral analysis differentiates between isotropic and anisotropic structures.

Structural characteristics influence network robustness and dynamics.

Abstract

A complex network is said to show topological isotropy if the topological structure around a particular node looks the same in all directions of the whole network. Topologically anisotropic networks are those where the local neighborhood around a node is not reproduced at large scale for the whole network. The existence of topological isotropy is investigated by the existence of a power-law scaling between a local and a global topological characteristic of complex networks obtained from graph spectra. We investigate this structural characteristic of complex networks and its consequences for 32 real-world networks representing informational, technological, biological, social and ecological systems.