HUSCAP logo Hokkaido Univ. logo

Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Engineering / Faculty of Engineering >
Peer-reviewed Journal Articles, etc >

A general model of hierarchical fractal scale-free networks

Files in This Item:

The file(s) associated with this item can be obtained from the following URL:

Title: A general model of hierarchical fractal scale-free networks
Authors: Yakubo, Kousuke Browse this author →KAKEN DB
Fujiki, Yuka Browse this author
Issue Date: 21-Mar-2022
Publisher: PLOS
Journal Title: PLoS ONE
Volume: 17
Issue: 3
Start Page: e0264589
Publisher DOI: 10.1371/journal.pone.0264589
Abstract: We propose a general model of unweighted and undirected networks having the scale-free property and fractal nature. Unlike the existing models of fractal scale-free networks (FSFNs), the present model can systematically and widely change the network structure. In this model, an FSFN is iteratively formed by replacing each edge in the previous generation network with a small graph called a generator. The choice of generators enables us to control the scale-free property, fractality, and other structural properties of hierarchical FSFNs. We calculate theoretically various characteristic quantities of networks, such as the exponent of the power-law degree distribution, fractal dimension, average clustering coefficient, global clustering coefficient, and joint probability describing the nearest-neighbor degree correlation. As an example of analyses of phenomena occurring on FSFNs, we also present the critical point and critical exponents of the bond-percolation transition on infinite FSFNs, which is related to the robustness of networks against edge removal. By comparing the percolation critical points of FSFNs whose structural properties are the same as each other except for the clustering nature, we clarify the effect of the clustering on the robustness of FSFNs. As demonstrated by this example, the present model makes it possible to elucidate how a specific structural property influences a phenomenon occurring on FSFNs by varying systematically the structures of FSFNs. Finally, we extend our model for deterministic FSFNs to a model of non-deterministic ones by introducing asymmetric generators and reexamine all characteristic quantities and the percolation problem for such non-deterministic FSFNs.
Type: article
Appears in Collections:工学院・工学研究院 (Graduate School of Engineering / Faculty of Engineering) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Export metadata:

OAI-PMH ( junii2 , jpcoar_1.0 )

MathJax is now OFF:


 - Hokkaido University