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Quantifying influential nodes in complex networks using optimization and particle dynamics: a comparative study

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Abstract

In this study, we propose a novel methodology called Particle Dynamics Method (PDM) for identifying and quantifying influential nodes in complex networks. Inspired by Newton’s three laws of motion and the universal gravitation law, PDM is based on a mathematical programming method that leverages node degrees and shortest path lengths. Unlike traditional centrality measures, PDM is easily adaptable to different network sizes and models, making it a versatile tool for network analysis. Our updated version of PDM also considers the direction of each force, resulting in more reliable results. To evaluate PDM’s performance, we tested it on a set of benchmark networks with distinct characteristics and models. Our results demonstrate that PDM outperforms other methodologies in the literature, as removing the identified influential nodes results in a significant decrease in network efficiency and robustness. The key feature of PDM is its flexibility in defining distance, which can be adapted to various network types. For instance, in a transportation network, distance can be defined by the flow between nodes, while in an academic publication system, the quartile of the journal could be used. Our research not only demonstrates the effectiveness of PDM but also highlights the influence of universities in the higher education and global university ranking networks, shedding light on the dynamics of these networks. Our interdisciplinary work has significant potential for collaborations between optimization, physics, and network science. This study opens up avenues for future research, including the extension of PDM to multilayer networks and the generalization of the metrics of monolayer networks for this purpose.

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Data availability

The data used to support the findings of this work, are available from the corresponding author upon request. However, we annex the URLs of each database: \(\cdot \) QSRanking 2018\(\cdot \) QSRanking 2019\(\cdot \) QSRanking 2020\(\cdot \) ExECUM 2014-2018

Notes

  1. In order for the reader to become familiar with the terms used in this work, Table 22 in Annex 1 shows a summary of the meanings of each one.

  2. It is important to note that all comparative results for this study are available in the next link.

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Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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Author notes

  1. E. Montes-Orozco, R.-A. Mora-Gutiérrez, S.-G. de-los-Cobos-Silva, E.-A. Rincón-García, Miguel-Ángel Gutiérrez-Andrade and P. Lara-Velázquez have contributed equally to this work.

Authors and Affiliations

  1. Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana Cuajimalpa, Av. Vasco de Quiroga 4871, Col. Santa Fe Cuajimalpa, 05348, Cuajimalpa, Mexico City, Mexico

    Edwin Montes-Orozco

  2. Departamento de Sistemas, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 420 Col. Nueva el Rosario, 02128, Azcapotzalco, Mexico City, Mexico

    Roman-Anselmo Mora-Gutiérrez

  3. Departamento de Ingeniería Eléctrica, Universidad Autónoma Metropolitana Iztapalapa, Av. Ferrocarril San Rafael Atlixco 186, Col. Leyes de Reforma, 09130, Iztapalapa, Mexico City, Mexico

    Sergio-Gerardo de-los-Cobos-Silva, Eric-Alfredo Rincón-García, Miguel-Ángel Gutiérrez-Andrade & Pedro Lara-Velázquez

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  1. Edwin Montes-Orozco
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Correspondence to Edwin Montes-Orozco.

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Appendix 1

Appendix 1

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Table 22 Table of used symbols
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Montes-Orozco, E., Mora-Gutiérrez, RA., de-los-Cobos-Silva, SG. et al. Quantifying influential nodes in complex networks using optimization and particle dynamics: a comparative study. Computing 106, 821–864 (2024). https://doi.org/10.1007/s00607-023-01244-z

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