Networks in life: Scaling properties and eigenvalue spectra

TL;DR

This paper investigates the structural properties of various biological and social networks, demonstrating their scale-free and hierarchical nature, and explores how eigenvalue spectra can classify small measured networks.

Contribution

It introduces a deterministic method to demonstrate scale-free and hierarchical features in diverse networks and applies eigenvalue spectra analysis for network categorization.

Findings

Networks exhibit scale-free and hierarchical organization.

Eigenvalue spectra can classify small networks effectively.

Deterministic constructions reveal structural properties.

Abstract

We analyse growing networks ranging from collaboration graphs of scientists to the network of similarities defined among the various transcriptional profiles of living cells. For the explicit demonstration of the scale-free nature and hierarchical organization of these graphs, a deterministic construction is also used. We demonstrate the use of determining the eigenvalue spectra of sparse random graph models for the categorization of small measured networks.