{"title":"Random multi-hooking networks","authors":"K. R. Bhutani, Ravi Kalpathy, H. Mahmoud","doi":"10.1017/s0269964822000523","DOIUrl":null,"url":null,"abstract":"\n We introduce a broad class of multi-hooking networks, wherein multiple copies of a seed are hooked at each step at random locations, and the number of copies follows a predetermined building sequence of numbers. We analyze the degree profile in random multi-hooking networks by tracking two kinds of node degrees—the local average degree of a specific node over time and the global overall average degree in the graph. The former experiences phases and the latter is invariant with respect to the type of building sequence and is somewhat similar to the average degree in the initial seed. We also discuss the expected number of nodes of the smallest degree. Additionally, we study distances in the network through the lens of the average total path length, the average depth of a node, the eccentricity of a node, and the diameter of the graph.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"15 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability in the Engineering and Informational Sciences","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1017/s0269964822000523","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, INDUSTRIAL","Score":null,"Total":0}
引用次数: 2
Abstract
We introduce a broad class of multi-hooking networks, wherein multiple copies of a seed are hooked at each step at random locations, and the number of copies follows a predetermined building sequence of numbers. We analyze the degree profile in random multi-hooking networks by tracking two kinds of node degrees—the local average degree of a specific node over time and the global overall average degree in the graph. The former experiences phases and the latter is invariant with respect to the type of building sequence and is somewhat similar to the average degree in the initial seed. We also discuss the expected number of nodes of the smallest degree. Additionally, we study distances in the network through the lens of the average total path length, the average depth of a node, the eccentricity of a node, and the diameter of the graph.
期刊介绍:
The primary focus of the journal is on stochastic modelling in the physical and engineering sciences, with particular emphasis on queueing theory, reliability theory, inventory theory, simulation, mathematical finance and probabilistic networks and graphs. Papers on analytic properties and related disciplines are also considered, as well as more general papers on applied and computational probability, if appropriate. Readers include academics working in statistics, operations research, computer science, engineering, management science and physical sciences as well as industrial practitioners engaged in telecommunications, computer science, financial engineering, operations research and management science.