Estimating and increasing the structural robustness of a network

Abstract

The capability of a network to cope with threats and survive attacks is referred to as its robustness. This article 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.

Perron communicability and sensitivity of multilayer networks

“…Several of the techniques discussed evaluate the exponential of the adjacency matrix of the network, or the exponential of the adjacency matrix determined by the line graph associated with the given network. The present paper extends the communicability and sensitivity analysis in [8,19] to multilayer networks. Since multilayer networks typically have a large number of nodes and edges, we focus on techniques that are well suited for large-scale networks.…”

Perron communicability and sensitivity of multilayer networks

“…Several of the techniques discussed evaluate the exponential of the adjacency matrix of the network, or the exponential of adjacency matrix determined by the line graph associated with the given network. The present paper extends the communicability and sensitivity analysis in [8,19] to multilayer networks. Since multilayer networks typically have a large number of nodes and edges, we focus on techniques that are well suited for large-scale networks.…”

“…The investigation of the importance of nodes and edges, as well as the sensitivity of the communicability within a network to changes in the edge weights of the network with only one kind of nodes and edges has received considerable attention in the literature; see, e.g., [4,5,8,9,10,11,12,17,19] and references therein. Several of the techniques discussed evaluate the exponential of the adjacency matrix of the network, or the exponential of adjacency matrix determined by the line graph associated with the given network.…”

The structured distance to singularity of a symmetric tridiagonal Toeplitz matrix

“…Measures of structured eigenvalue sensitivity include both structured pseudospectra (see, e.g., [11,30,7,17,3,25]) and structured condition numbers, introduced by Tisseur [35]. The latter measures have been investigated, e.g., in [18,22,24,2] and, recently, applied to network analysis [28,10].…”