D-summable fractal dimensions of complex networks

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

Research output: Contribution to journalArticleResearchpeer-review

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.

Original languageEnglish
Pages (from-to)210-214
Number of pages5
JournalChaos, Solitons and Fractals
Volume119
DOIs
StatePublished - 1 Feb 2019

Fingerprint

Complex networks
Fractal dimension
Fractal Dimension
Complex Networks
fractals
Large scale systems
Topology
Geometric Measure Theory
Box Dimension
boxes
Correlation Dimension
Network Topology
Complex Systems
Covering
complex systems
Calculate
coverings
topology
Model
Range of data

Keywords

  • Box-counting algorithm
  • Complex networks
  • D-summability
  • Fractals
  • Information dimensions

Cite this

Ramirez-Arellano, Aldo ; Bermúdez-Gómez, Salvador ; Hernández-Simón, Luis Manuel ; Bory-Reyes, Juan. / D-summable fractal dimensions of complex networks. In: Chaos, Solitons and Fractals. 2019 ; Vol. 119. pp. 210-214.
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D-summable fractal dimensions of complex networks. / Ramirez-Arellano, Aldo; Bermúdez-Gómez, Salvador; Hernández-Simón, Luis Manuel; Bory-Reyes, Juan.

In: Chaos, Solitons and Fractals, Vol. 119, 01.02.2019, p. 210-214.

Research output: Contribution to journalArticleResearchpeer-review

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