# Francesca ArrigoUniversity of Strathclyde · Department of Mathematics and Statistics

Francesca Arrigo

Ph.D.

## About

23

Publications

3,389

Reads

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266

Citations

Citations since 2016

Introduction

**Skills and Expertise**

Additional affiliations

May 2019 - May 2022

## Publications

Publications (23)

We study walk-based centrality measures for time-ordered network sequences. For the case of standard dynamic walk-counting, we show how to derive and compute centrality measures induced by analytic functions. We also prove that dynamic Katz centrality, based on the resolvent function, has the unique advantage of allowing computations to be performe...

We extend the notion of nonbacktracking walks from unweighted graphs to graphs whose edges have a nonnegative weight. Here the weight associated with a walk is taken to be the product over the weights along the individual edges. We give two ways to compute the associated generating function, and corresponding node centrality measures. One method wo...

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 cases well-known centrality measures like subgraph centrality and Katz centrality. The indices we introduce are parametrized by two numbers; by letting these vary, we show tha...

We study walk-based centrality measures for time-ordered network sequences. For the case of standard dynamic walk-counting, we show how to derive and compute centrality measures induced by analytic functions. We also prove that dynamic Katz centrality, based on the resolvent function, has the unique advantage of allowing computations to be performe...

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 cases well-known centrality measures like subgraph centrality and Katz centrality. The indices we introduce are parametrized by two numbers; by letting these vary, we show that...

We develop a complete theory for the combinatorics of walk-counting on a directed graph in the case where each backtracking step is downweighted by a given factor. By deriving expressions for the associated generating functions, we also obtain linear systems for computing centrality measures in this setting. In particular, we show that backtrack-do...

We propose and analyse a general tensor-based framework for incorporating second-order features into network measures. This approach allows us to combine traditional pairwise links with information that records whether triples of nodes are involved in wedges or triangles. Our treatment covers classical spectral methods and recently proposed cases f...

Walks around a graph are studied in a wide range of fields, from graph theory and stochastic analysis to theoretical computer science and physics. In many cases it is of interest to focus on non-backtracking walks; those that do not immediately revisit their previous location. In the network science context, imposing a non-backtracking constraint o...

We propose and analyse a general tensor-based framework for incorporating second order features into network measures. This approach allows us to combine traditional pairwise links with information that records whether triples of nodes are involved in wedges or triangles. Our treatment covers classical spectral methods and recently proposed cases f...

The PageRank algorithm, which has been “bringing order to the web” for more than 20 years, computes the steady state of a classical random walk plus teleporting. Here we consider a variation of PageRank that uses a non-backtracking random walk. To do this, we first reformulate PageRank in terms of the associated line graph. A non-backtracking analo...

We derive an explicit formula for the exponential generating function associated with non-backtracking walks around a graph. We study both undirected and directed graphs. Our results allow us to derive computable expressions for non-backtracking versions of network centrality measures based on the matrix exponential. We find that eliminating backtr...

We introduce a ranking model for temporal multi-dimensional weighted and directed networks based on the Perron eigenvector of a multi-homogeneous order-preserving map. The model extends to the temporal multilayer setting the HITS algorithm and defines five centrality vectors: two for the nodes, two for the layers, and one for the temporal stamps. N...

The theory of zeta functions provides an expression for the generating function of non-backtracking walk counts on a directed network. We show how this expression can be used to produce a centrality measure that eliminates backtracking walks at no cost. We also show that the radius of convergence of the generating function is related to the spectru...

Time sliced networks describing human-human digital interactions are typically large and sparse. This is the case, for example, with pairwise connectivity describing social media, voice call or physical proximity, when measured over seconds, minutes or hours. However, if we wish to quantify and compare the overall time-dependent centrality of the n...

Time sliced networks describing human-human digital interactions are typically large and sparse. This is the case, for example, with pairwise connectivity describing social media, voice call or physical proximity, when measured over seconds, minutes or hours. However, if we wish to quantify and compare the overall time-dependent centrality of the n...

Eigenvector-based centrality measures are among the most popular centrality measures in network science. The underlying idea is intuitive and the mathematical description is extremely simple in the framework of standard, mono-layer networks. Moreover, several efficient computational tools are available for their computation. Moving up in dimensiona...

We develop numerical algorithms for the efficient evaluation of quantities
associated with generalized matrix functions [J. B. Hawkins and A. Ben-Israel,
Linear and Multilinear Algebra 1(2), 1973, pp. 163-171]. Our algorithms are
based on Gaussian quadrature and Golub--Kahan bidiagonalization. Block variants
are also investigated. Numerical experim...

We introduce new broadcast and receive communicability indices that can be used as global measures of how effectively information is spread in a directed network. Furthermore, we describe fast and effective criteria for the selection of edges to be added to (or deleted from) a given directed network so as to enhance these network communicability me...

We propose a communication-driven mechanism for predicting triadic closure in
complex networks. It is mathematically formulated on the basis of
communicability distance functions that account for the "goodness" of
communication between nodes in the network. We study $25$ real-world networks
and show that the proposed method predicts correctly $20\%...

The total communicability of a network (or graph) is defined as the sum of
the entries in the exponential of the adjacency matrix of the network, possibly
normalized by the number of nodes. This quantity offers a good measure of how
easily information spreads across the network, and can be useful in the design
of networks having certain desirable p...