Estimating and increasing the structural robustness of a network

TL;DR

This paper explores methods to enhance network robustness by reducing the spectral radius of its adjacency matrix, using computational techniques and pseudospectra analysis, with applications including pandemic-related social networks.

Contribution

It introduces computational approaches for identifying edges whose removal decreases spectral radius, especially in nonsymmetric matrices relevant to real-world networks.

Findings

Edge removal can significantly reduce spectral radius.

Pseudospectra analysis aids in understanding nonsymmetric matrices.

Methods applicable to networks like social interactions during Covid-19.

Abstract

The capability of a network to cope with threats and survive attacks is referred to as its robustness. This paper discusses one kind of robustness, commonly denoted structural robustness, which increases when the spectral radius of the adjacency matrix associated with the network decreases. We discuss computational techniques for identifying edges, whose removal may significantly reduce the spectral radius. Nonsymmetric adjacency matrices are studied with the aid of their pseudospectra. In particular, we consider nonsymmetric adjacency matrices that arise when people seek to avoid being infected by Covid-19 by wearing facial masks of different qualities.