Moment-Based Spectral Analysis of Large-Scale Networks Using Local Structural Information

TL;DR

This paper introduces a novel method leveraging algebraic graph theory and convex optimization to analyze how local structural properties of large networks influence their eigenvalue spectra, avoiding limitations of synthetic models.

Contribution

It presents a new approach that computes global spectral properties from local structural information without relying on synthetic network models.

Findings

Efficient computation of spectral properties from local data

Insights into the influence of social network structures on eigenvalues

Overcomes limitations of traditional synthetic network models

Abstract

The eigenvalues of matrices representing the structure of large-scale complex networks present a wide range of applications, from the analysis of dynamical processes taking place in the network to spectral techniques aiming to rank the importance of nodes in the network. A common approach to study the relationship between the structure of a network and its eigenvalues is to use synthetic random networks in which structural properties of interest, such as degree distributions, are prescribed. Although very common, synthetic models present two major flaws: (\emph{i}) These models are only suitable to study a very limited range of structural properties, and (\emph{ii}) they implicitly induce structural properties that are not directly controlled and can deceivingly influence the network eigenvalue spectrum. In this paper, we propose an alternative approach to overcome these limitations. Our approach is not based on synthetic models, instead, we use algebraic graph theory and convex optimization to study how structural properties influence the spectrum of eigenvalues of the network. Using our approach, we can compute with low computational overhead global spectral properties of a network from its local structural properties. We illustrate our approach by studying how structural properties of online social networks influence their eigenvalue spectra.