TY - JOUR
T1 - D-summable fractal dimensions of complex networks
AU - Ramirez-Arellano, Aldo
AU - Bermúdez-Gómez, Salvador
AU - Hernández-Simón, Luis Manuel
AU - Bory-Reyes, Juan
N1 - Publisher Copyright:
© 2019 Elsevier Ltd
PY - 2019/2
Y1 - 2019/2
N2 - 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.
AB - 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.
KW - Box-counting algorithm
KW - Complex networks
KW - D-summability
KW - Fractals
KW - Information dimensions
UR - http://www.scopus.com/inward/record.url?scp=85059551461&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2018.12.026
DO - 10.1016/j.chaos.2018.12.026
M3 - Artículo
AN - SCOPUS:85059551461
SN - 0960-0779
VL - 119
SP - 210
EP - 214
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
ER -