Título:
Finding the resistance distance and eigenvector centrality from the network’s eigenvalues
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Autor:
Gutiérrez Ibarra, Caracé
Gancio Vázquez, Juan
Cabeza, Cecilia
Rubido, Nicolás
Gancio Vázquez, Juan
Cabeza, Cecilia
Rubido, Nicolás
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Tipo de documento:
Preprint
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Palabras clave:
Resistor networks
Resistor distance
Eigenvector centrality
Eigenvalue spectra
Resistor distance
Eigenvector centrality
Eigenvalue spectra
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Año de publicación:
2020
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Resumen:
There are different measures to classify a network's data set that, depending on the problem, have different success. For example, the resistance distance and eigenvector centrality measures have been successful in revealing ecological pathways and differentiating between biomedical images of patients with Alzheimer's disease, respectively. The resistance distance measures the effective distance between any two nodes of a network taking into account all possible shortest paths between them and the eigenvector centrality measures the relative importance of each node in the network. However, both measures require knowing the network's eigenvalues and eigenvectors -- eigenvectors being the more computationally demanding task. Here, we show that we can closely approximate these two measures using only the eigenvalue spectra, where we illustrate this by experimenting on elemental resistor circuits and paradigmatic network models -- random and small-world networks. Our results are supported by analytical derivations, showing that the eigenvector centrality can be perfectly matched in all cases whilst the resistance distance can be closely approximated. Our underlying approach is based on the work by Denton, Parke, Tao, and Zhang [arXiv:1908.03795 (2019)], which is unrestricted to these topological measures and can be applied to most problems requiring the calculation of eigenvectors.
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Publicado también en: Physica A: Statistical Mechanics and its Applications, 2021, 569: 125751. DOI: 10.1016/j.physa.2021.125751.
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arXiv
EN:
Physics (Physics and Society), arXiv:2005.00452, May 2020, pp 1-7.
Financiadores:
ANII: POS_NAC_2018_1_151237
ANII: POS_NAC_2018_1_151185
CSIC: 2018 - FID13 - grupo ID 722
ANII: POS_NAC_2018_1_151185
CSIC: 2018 - FID13 - grupo ID 722
Citación:
Gutiérrez Ibarra, C, Gancio Vázquez, J, Cabeza, C [y otro autor]. "Finding the resistance distance and eigenvector centrality from the network’s eigenvalues". [preprint] Publicado en: Physics (Physics and Society). 2020, arXiv:2005.00452, May 2020, pp 1-7. DOI: 10.48550/arXiv.2005.00452.
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Licencia Creative Commons Atribución (CC - By 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| 101016jphysa2021125751.pdf | — | 2.33 MB | Adobe PDF |