Volume Dimension of Mass Functions in Complex Networks

Maria del Carmen Soto-Camacho, Jazmin Susana De la Cruz-Garcia, Juan Bory-Reyes and Aldo Ramirez-Arellano ()
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Maria del Carmen Soto-Camacho: Sección de Estudios de Posgrado e Investigación, Unidad Profesional Interdisciplinaria de Ingeniería y Ciencias Sociales y Administrativas, Instituto Politécnico Nacional, Mexico City 08400, Mexico
Jazmin Susana De la Cruz-Garcia: Sección de Estudios de Posgrado e Investigación, Escuela Superior de Ingeniería Mecánica y Eléctrica (Zacatenco), Instituto Politécnico Nacional, Mexico City 07338, Mexico
Juan Bory-Reyes: Sección de Estudios de Posgrado e Investigación, Escuela Superior de Ingeniería Mecánica y Eléctrica (Zacatenco), Instituto Politécnico Nacional, Mexico City 07338, Mexico
Aldo Ramirez-Arellano: Sección de Estudios de Posgrado e Investigación, Unidad Profesional Interdisciplinaria de Ingeniería y Ciencias Sociales y Administrativas, Instituto Politécnico Nacional, Mexico City 08400, Mexico

Mathematics, 2025, vol. 13, issue 17, 1-29

Abstract: A novel definition of volume dimension for a mass function based on a sigmoid asymptote is proposed; in particular, we extend the volume dimension of a mass function to define the volume dimensions for nodes and edges in complex networks. Furthermore, the relationship between the proposed volume dimension and the non-specificity term of the Deng entropy is shown, and the traditional volume dimension and volume dimension based on the node degree in complex networks are revisited. Our experiments show that in both real and synthetic complex networks, the volume dimension tends to follow a sigmoidal asymptote rather than the previously utilized power law asymptote.

Keywords: complex networks; volume dimension; sigmoid asymptote; mass function; evidence theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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