Can the PageRank centrality be manipulated to obtain any desired ranking?

The significance of the PageRank algorithm in shaping the modern Internet cannot be overstated, and its Complex Network theory foundations continue to be a subject of research. In this article we carry out a systematic study of the structural and parametric controllability of PageRank's outcomes, translating a spectral Graph Theory problem into a geometric one, where a natural characterization of its rankings emerges. Furthermore, we show that the change of perspective employed can be applied to the biplex PageRank proposal, performing numerical computations on both real and synthetic network datasets to compare centrality measures used.Comment: 18 pages, 6 figure

A biplex approach to PageRank centrality: from classic to multiplex networks

In this paper, we present a new view of the PageRank algorithm inspired by multiplex networks. This new approach allows to introduce a new centrality measure for classic complex networks and a new proposal to extend the usual PageRank algorithm to multiplex networks. We give some analytical relations between these new approaches and the classic PageRank centrality measure, and we illustrate the new parameters presented by computing them on real underground networks. © 2016 Author(s).This work has been partially supported by the project MTM2014-59906 (Spanish Ministry) and the Grant URJC-Grupo de Excelencia Investigadora GARECOM (2014-2016).Pedroche Sánchez, F.; Romance, M.; Criado Herrero, R. (2016). A biplex approach to PageRank centrality: from classic to multiplex networks. Chaos. 26(6):065301-1-065301-9. https://doi.org/10.1063/1.4952955S065301-1065301-926

On the spectrum of two-layer approach and Multiplex PageRank

[EN] In this paper, we present some results about the spectrum of the matrix associated with the computation of the Multiplex PageRank defined by the authors in a previous paper. These results can be considered as a natural extension of the known results about the spectrum of the Google matrix. In particular, we show that the eigenvalues of the transition matrix associated with the multiplex network can be deduced from the eigenvalues of a block matrix containing the stochastic matrices defined for each layer. We also show that, as occurs in the classic PageRank, the spectrum is not affected by the personalization vectors defined on each layer but depends on the parameter a that controls the teleportation. We also give some analytical relations between the eigenvalues and we include some small examples illustrating the main results. (C) 2018 Elsevier B.V. All rights reserved.We thank the two anonymous reviewers for their constructive comments, which helped us to improve the manuscript. This work has been partially supported by the projects MTM2014-59906-P, MTM2014-52470-P (Spanish Ministry and FEDER, EU, Spain), MTM2017-84194-P (AEI/FEDER, EU, Spain) and the grant URJC-Grupo de Excelencia Investigadora GARECOM (2014-2017), Spain.Pedroche Sánchez, F.; García, E.; Romance, M.; Criado Herrero, R. (2018). On the spectrum of two-layer approach and Multiplex PageRank. Journal of Computational and Applied Mathematics. 344:161-172. https://doi.org/10.1016/j.cam.2018.05.033S16117234

Sharp estimates for the personalized Multiplex PageRank

[EN] PageRank can be understood as the stationary distribution of a Markov chain that occurs in a two-layer network with the same set of nodes in both layers: the physical layer and the teleportation layer. In this paper we present some bounds for the extension of this two-layer approach to Multiplex networks, establishing sharp estimates for this Multiplex PageRank and locating the possible values of the personalized PageRank for each node of a network. Several examples are shown to compare the values obtained for both algorithms, the classic and the two-layer PageRank. (C) 2017 Elsevier B.V. All rights reserved.This work has been partially supported by the projects MTM2014-59906-P, MTM2014-52470-P (Spanish Ministry) and the grant Grupo de excelencia investigadora URJC-Banco de Santander GARECOM 30VCPIGI11. The authors would like to thank an anonymous referee for his/her valuable comments and remarks that have improved the readability of the manuscript.Pedroche Sánchez, F.; García, E.; Romance, M.; Criado Herrero, R. (2018). Sharp estimates for the personalized Multiplex PageRank. Journal of Computational and Applied Mathematics. 330:1030-1040. https://doi.org/10.1016/j.cam.2017.02.013S1030104033

Some rankings based on PageRank applied to the Valencia Metro

[EN] In this paper we apply a recent model of Multiplex PageRank to the multiplex network formed with the 9 lines of the metro of Valencia (Spain). We compute the PageRank vector following di erent approaches and we compare the results with those recently obtained for the Madrid metro system.This work has been partially supported by the project MTM2014-59906 (Spanish Ministry) and the grant URJC-Grupo de Excelencia Investigadora GARECOM (2014-2016).Pedroche Sánchez, F.; Romance, M.; Criado, R. (2016). Some rankings based on PageRank applied to the Valencia Metro. International Journal of Complex Systems in Science. 6(1):69-77. http://hdl.handle.net/10251/80968S69776

Comparing series of rankings with ties by using complex networks: An analysis of the Spanish stock market (IBEX-35 index)

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in [Networks and Heterogeneous Media] following peer review. The definitive publisher-authenticated version [Pedroche, F… (et al.) (2015). Comparing series of rankings with ties by using complex networks: An analysis of the Spanish stock market (IBEX-35 index). Springfield, MO: American Institute of Mathematical Science. Networks and Heterogeneous Media.Volume 10, Number 1, March 2015, pp. 101-125. eISSN 1556-181X] is available online at: https://aimsciences.org/journals/pdfs.jsp?paperID=10842&mode=fullIn this paper we extend the concept of Competitivity Graph to compare series of rankings with ties (partial rankings). We extend the usual method used to compute Kendall's coe cient for two partial rankings to the concept of evolutive Kendall's coe cient for a series of partial rankings. The theoretical framework consists of a four-layer multiplex network. Regarding the treatment of ties, our approach allows to de ne a tie between two values when they are close enough, depending on a threshold. We show an application using data from the Spanish Stock Market; we analyse the series of rankings de ned by 25 companies that have contributed to the IBEX-35 return and volatility values over the period 2003 to 2013.This work was partially supported by Spanish MICINN Funds and FEDER Funds MTM2009-13848, MTM2010-16153 and MTM2010-18674, and Junta de Andalucia Funds FQM-264. The authors would like to thank the referees for their valuable comments and remarks.Pedroche Sánchez, F.; Criado, R.; García, EH.; Romance, M.; Sánchez, VE. (2015). Comparing series of rankings with ties by using complex networks: An analysis of the Spanish stock market (IBEX-35 index). Networks and Heterogeneous Media. 10(1):101-125. https://doi.org/10.3934/nhm.2015.10.101S10112510