Spectral Perturbation and Reconstructability of Complex Networks

TL;DR

This paper introduces a new global measure called the reconstructability coefficient for complex networks, revealing a universal linear scaling law that relates network size to eigenvalue removability.

Contribution

It proposes a novel measure for network robustness and uncovers a universal linear relationship between network size and eigenvalue removability.

Findings

The reconstructability coefficient measures how many eigenvalues can be removed while preserving the adjacency matrix.

A universal linear scaling law, E[θ]=aN, applies across various studied networks.

The measure provides a new way to evaluate and compare network robustness.

Abstract

In recent years, many network perturbation techniques, such as topological perturbations and service perturbations, were employed to study and improve the robustness of complex networks. However, there is no general way to evaluate the network robustness. In this paper, we propose a new global measure for a network, the reconstructability coefficient {\theta}, defined as the maximum number of eigenvalues that can be removed, subject to the condition that the adjacency matrix can be reconstructed exactly. Our main finding is that a linear scaling law, E[{\theta}]=aN, seems universal, in that it holds for all networks that we have studied.