On PageRank versatility for multiplex networks: properties and some useful bounds

Pedroche, Francisco; Criado, Regino; Flores, Julio; Garcı́a, Esther; Romance, Miguel

doi:10.1002/mma.6274

Cited by 4 publications

(2 citation statements)

References 38 publications

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“…The damping factor is set to 𝛼 = 0.99, which is a difficult test case to solve and thus it may amplify round-off errors. To cover cases with small and relatively large dimensions, the restart value m is set to m = [3,6,9,15,20]. The four web adjacency matrices cnr-2000, web-NotreDame, web-BerkStan and eu-2005 are used as testbeds in our experiments.…”

Section: Example 61mentioning

confidence: 99%

“…The model can be thought of as a network centrality measure that allows us to identify the most important nodes within a large graph, 11 such as those that arise in the analysis of multiplex networks (see References 12‐15) or large micro‐array experiments in biology. Morrison et al, for example, proposed a GeneRank variant that can score the most relevant genes in a microarray experiment or in relation to a disease by combining gene expression information derived from gene annotations or expression profile correlations 16 .…”

Section: Introductionmentioning

confidence: 99%

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Preconditioned weighted full orthogonalization method for solving singular linear systems from PageRank problems

Shen,

Carpentieri,

Wen

et al. 2023

Numerical Linear Algebra App

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The PageRank model, which was first proposed by Google for its web search engine application, has since become a popular computational tool in a wide range of scientific fields, including chemistry, bioinformatics, neuroscience, bibliometrics, social networks, and others. PageRank calculations necessitate the use of fast computational techniques with low algorithmic and memory complexity. In recent years, much attention has been paid to Krylov subspace algorithms for solving difficult PageRank linear systems, such as those with large damping parameters close to one. In this article, we examine the full orthogonalization method (FOM). We present a convergence study of the method that extends and clarifies part of the conclusions reached in Zhang et al. (J Comput Appl Math. 2016; 296:397–409.). Furthermore, we demonstrate that FOM is breakdown free when solving singular PageRank linear systems with index one and we investigate the effect of using weighted inner‐products instead of conventional inner‐products in the orthonormalization procedure on FOM convergence. Finally, we develop a shifted polynomial preconditioner that takes advantage of the special structure of the PageRank linear system and has a good ability to cluster most of the eigenvalues, making it a good choice for an iterative method like FOM or GMRES. Numerical experiments are presented to support the theoretical findings and to evaluate the performance of the new weighted preconditioned FOM PageRank solver in comparison to other established solvers for this class of problem, including conventional stationary methods, hybrid combinations of stationary and Krylov subspace methods, and multi‐step splitting strategies.

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Section: Example 61mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Preconditioned weighted full orthogonalization method for solving singular linear systems from PageRank problems

Shen,

Carpentieri,

Wen

et al. 2023

Numerical Linear Algebra App

View full text Add to dashboard Cite

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A new insight into linguistic pattern analysis based on multilayer hypergraphs for the automatic extraction of text summaries

Criado-Alonso

Aleja

Romance

et al. 2023

Math Methods in App Sciences

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Forensic linguistics and stylometry have in the exploration of linguistic patterns one of their fundamental tools. Mathematical structures such as complex multilayer networks and hypergraphs provide remarkable resources to represent and analyze texts. In this paper, we present a model that includes some specific mesoscopic relations between the different types of words in a corpus (lexical words, verbs, linking words, other words) according to the sentences or paragraphs in which they appear. This model is supported by various mathematical structures such as partial multiline graphs, multilayer hypergraphs, and their derivative graphs. The methodology proposed from this new point of view is of singular help to find meaningful sentences from any text to set up an automatic summary of the text and, eventually, to determine its linguistic level.

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Identifying Influential Nodes in Complex Networks Based on Local and Global Methods

Mijia¹,

Wei²,

Li³

et al. 2021

J. Phys.: Conf. Ser.

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Identifying Influential Nodes in complex networks is of great significance in both theory and reality. K-shell decomposition method is a local method which is suitable for increasing scale of complex networks but limited in accuracy because many nodes are partitioned with the same K-shell value. To overcome the coarse result of K-shell, an improved K-shell which considers the number of nodes’ iteration layers and degrees is proposed. Unlike local methods, global methods such as Betweenness Centralities (BC) are accurate but time-consuming. We employed an algorithm framework which combines advantages of both local and global methods where core network is extracted by improved K-shell and then BC is used to quantitatively analyze nodes in the core network. We compare the proposed method with other existing methods on Susceptible-Infective-Removal (SIR) mode. Experiments on three real networks show that the proposed method is more efficient and accurate.

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On PageRank versatility for multiplex networks: properties and some useful bounds

Cited by 4 publications

References 38 publications

Preconditioned weighted full orthogonalization method for solving singular linear systems from PageRank problems

Preconditioned weighted full orthogonalization method for solving singular linear systems from PageRank problems

A new insight into linguistic pattern analysis based on multilayer hypergraphs for the automatic extraction of text summaries

Identifying Influential Nodes in Complex Networks Based on Local and Global Methods

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