D-summable fractal dimensions of complex networks

Aldo Ramirez-Arellano, Salvador Bermúdez-Gómez, Luis Manuel Hernández-Simón and Juan Bory-Reyes

Chaos, Solitons & Fractals, 2019, vol. 119, issue C, 210-214

Abstract: In past two decades a wide range of complex systems, spanning many different disciplines, have been structured in the form of networks. Network dimension is a crucial concept to understand not only network topology, but also dynamical processes on networks. From the perspective of the box covering, volume dimension, information dimension, and correlation dimension several approaches have been proposed. We modify the commonly used definitions of the box dimension and information dimension to introduce a d-summable approach (a geometric notion that comes from geometric measure theory) of these dimensions. It is applied to calculate d-summable information dimension of several real complex networks. We offer empirical evidence to support the conjecture that d-summable information model worth carrying out than information model for several networks.

Keywords: Fractals; Information dimensions; D-summability; Complex networks; Box-counting algorithm (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:119:y:2019:i:c:p:210-214

DOI: 10.1016/j.chaos.2018.12.026

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