{"title":"An enumeration approach to network evolution","authors":"G. Bacsó, J. Túri","doi":"10.18514/mmn.2023.4133","DOIUrl":null,"url":null,"abstract":". A simple theoretical model of network evolution is discussed here. In each step, we add a new vertex to the graph and it is allowed to connect it to maximum degree vertices (hubs) only. Given a constant p , the probability of such a connection is p for any hub. The initial (non-random) graph G 1 is arbitrary but here we investigate mostly the case when G 1 has one vertex. We solve here some particular cases of the problem, using enumeration methods. We obtain not limit theorems but exact results for the parameters discussed.","PeriodicalId":49806,"journal":{"name":"Miskolc Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Miskolc Mathematical Notes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.18514/mmn.2023.4133","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
. A simple theoretical model of network evolution is discussed here. In each step, we add a new vertex to the graph and it is allowed to connect it to maximum degree vertices (hubs) only. Given a constant p , the probability of such a connection is p for any hub. The initial (non-random) graph G 1 is arbitrary but here we investigate mostly the case when G 1 has one vertex. We solve here some particular cases of the problem, using enumeration methods. We obtain not limit theorems but exact results for the parameters discussed.
期刊介绍：
Miskolc Mathematical Notes, HU ISSN 1787-2405 (printed version), HU ISSN 1787-2413 (electronic version), is a peer-reviewed international mathematical journal aiming at the dissemination of results in many fields of pure and applied mathematics.
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