Network Model with Scale-Free, High Clustering Coefficients, and Small-World Properties

Networks are prevalent in real life, and the study of network evolution models is very important for understanding the nature and laws of real networks. The distribution of the initial degree of nodes in existing classical models is constant or uniform. The model we proposed shows binomial distribut...

Full description

Saved in:
Bibliographic Details
Main Author: Chuankui Yan
Format: Article
Language:English
Published: Wiley 2023-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2023/5533260
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849470951921549312
author Chuankui Yan
author_facet Chuankui Yan
author_sort Chuankui Yan
collection DOAJ
description Networks are prevalent in real life, and the study of network evolution models is very important for understanding the nature and laws of real networks. The distribution of the initial degree of nodes in existing classical models is constant or uniform. The model we proposed shows binomial distribution, and it is consistent with real network data. The theoretical analysis shows that the proposed model is scale-free at different probability values and its clustering coefficients are adjustable, and the Barabasi-Albert model is a special case of p=0 in our model. In addition, the analytical results of the clustering coefficients can be estimated using mean-field theory. The mean clustering coefficients calculated from the simulated data and the analytical results tend to be stable. The model also exhibits small-world characteristics and has good reproducibility for short distances of real networks. Our model combines three network characteristics, scale-free, high clustering coefficients, and small-world characteristics, which is a significant improvement over traditional models with only a single or two characteristics. The theoretical analysis procedure can be used as a theoretical reference for various network models to study the estimation of clustering coefficients. The existence of stable equilibrium points of the model explains the controversy of whether scale-free is universal or not, and this explanation provides a new way of thinking to understand the problem.
format Article
id doaj-art-da6538e46d604e85a4eeddb49d343d94
institution Kabale University
issn 1687-0042
language English
publishDate 2023-01-01
publisher Wiley
record_format Article
series Journal of Applied Mathematics
spelling doaj-art-da6538e46d604e85a4eeddb49d343d942025-08-20T03:24:59ZengWileyJournal of Applied Mathematics1687-00422023-01-01202310.1155/2023/5533260Network Model with Scale-Free, High Clustering Coefficients, and Small-World PropertiesChuankui Yan0College of Mathematics and PhysicsNetworks are prevalent in real life, and the study of network evolution models is very important for understanding the nature and laws of real networks. The distribution of the initial degree of nodes in existing classical models is constant or uniform. The model we proposed shows binomial distribution, and it is consistent with real network data. The theoretical analysis shows that the proposed model is scale-free at different probability values and its clustering coefficients are adjustable, and the Barabasi-Albert model is a special case of p=0 in our model. In addition, the analytical results of the clustering coefficients can be estimated using mean-field theory. The mean clustering coefficients calculated from the simulated data and the analytical results tend to be stable. The model also exhibits small-world characteristics and has good reproducibility for short distances of real networks. Our model combines three network characteristics, scale-free, high clustering coefficients, and small-world characteristics, which is a significant improvement over traditional models with only a single or two characteristics. The theoretical analysis procedure can be used as a theoretical reference for various network models to study the estimation of clustering coefficients. The existence of stable equilibrium points of the model explains the controversy of whether scale-free is universal or not, and this explanation provides a new way of thinking to understand the problem.http://dx.doi.org/10.1155/2023/5533260
spellingShingle Chuankui Yan
Network Model with Scale-Free, High Clustering Coefficients, and Small-World Properties
Journal of Applied Mathematics
title Network Model with Scale-Free, High Clustering Coefficients, and Small-World Properties
title_full Network Model with Scale-Free, High Clustering Coefficients, and Small-World Properties
title_fullStr Network Model with Scale-Free, High Clustering Coefficients, and Small-World Properties
title_full_unstemmed Network Model with Scale-Free, High Clustering Coefficients, and Small-World Properties
title_short Network Model with Scale-Free, High Clustering Coefficients, and Small-World Properties
title_sort network model with scale free high clustering coefficients and small world properties
url http://dx.doi.org/10.1155/2023/5533260
work_keys_str_mv AT chuankuiyan networkmodelwithscalefreehighclusteringcoefficientsandsmallworldproperties