Approximating the largest eigenvalue of network adjacency matrices

TL;DR

This paper develops and compares approximation methods for the largest eigenvalue of network adjacency matrices, which are crucial for understanding various network dynamics, validated through numerical experiments on simulated networks.

Contribution

It introduces new approximation techniques for the largest eigenvalue and analyzes their relationships, enhancing understanding of spectral properties in networks.

Findings

New approximation methods for the largest eigenvalue.

Relationships between different approximations analyzed.

Numerical validation on simulated networks confirms effectiveness.

Abstract

The largest eigenvalue of the adjacency matrix of a network plays an important role in several network processes (e.g., synchronization of oscillators, percolation on directed networks, linear stability of equilibria of network coupled systems, etc.). In this paper we develop approximations to the largest eigenvalue of adjacency matrices and discuss the relationships between these approximations. Numerical experiments on simulated networks are used to test our results.