We review the recent use of functions of matrices in the analysis of graphs and networks,
with special focus on centrality and communicability measures and diffusion processes. Both …

The computation of matrix functions f(A), or related quantities like their trace, is an important
but challenging task, in particular, for large and sparse matrices A. In recent years, probing …

We describe a complete theory for walk-based centrality indices in complex networks
defined in terms of Mittag--Leffler functions. This overarching theory includes as special …

We consider the task of updating a matrix function f(A) when the matrix A∈C^n*n is subject
to a low-rank modification. In other words, we aim at approximating f(A+D)-f(A) for a matrix D …

Creative influence is responsible for a considerable part of the creative process of an artist
and can largely be associated with their social circle. It has been observed that the type and …

When analyzing complex networks, an important task is the identification of those nodes
which play a leading role for the overall communicability of the network. In the context of …

This work is concerned with approximating matrix functions for banded matrices,
hierarchically semiseparable matrices, and related structures. We develop a new divide-and …

This paper derives a priori residual-type bounds for the Arnoldi approximation of a matrix
function together with a strategy for setting the iteration accuracies in the inexact Arnoldi …

In this work we introduce and study a nonlocal version of the PageRank. In our approach,
the random walker explores the graph using longer excursions than just moving between …

We consider the problem of attaining either the maximal increase or reduction of the
robustness of a complex network by means of a bounded modification of a subset of the …