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A novel approach to estimated Boulingand-Minkowski fractal dimension from complex networks

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Author(s):
de Sa, Luiz Alberto Pereira ; Zielinski, Kallil M. C. ; Rodrigues, Erick Oliveira ; Backes, Andre R. ; Florindo, Joao B. ; Casanova, Dalcimar
Total Authors: 6
Document type: Journal article
Source: CHAOS SOLITONS & FRACTALS; v. 157, p. 10-pg., 2022-04-01.
Abstract

A complex network presents many topological features which characterize its behavior and dynamics. This characterization is an essential aspect of complex networks analysis and can be performed using sev-eral measures, including the fractal dimension. Originally the fractal dimension measures the complexity of an object in a Euclidean space, and the most common methods in the literature to estimate that di-mension are box-counting, mass-radius, and Bouligand-Minkowski. However, networks are not Euclidean objects, so that these methods require some adaptation to measure the fractal dimension in this con -text. The literature presents some adaptations for methods like box-counting and mass-radius. However, there is no known adaptation developed for the Bouligand-Minkowski method. In this way, we propose an adaptation of the Bouligand-Minkowski to measure complex networks' fractal dimension. We com-pare our proposed method with others, and we also explore the application of the proposed method in a classification task of complex networks that confirmed its promising potential.(c) 2022 Elsevier Ltd. All rights reserved. (AU)

FAPESP's process: 20/01984-8 - Introducing elements of fractal geometry into deep convolutional neural networks: an application to the recognition and categorization of Lung Cancer
Grantee:Joao Batista Florindo
Support Opportunities: Regular Research Grants