{"title":"The small-world phenomenon: a model, explanations, characterizations, and examples","authors":"Leo Egghe, Ronald Rousseau","doi":"10.1007/s11192-024-05119-8","DOIUrl":null,"url":null,"abstract":"<p>We introduce and define three types of small worlds: small worlds based on the diameter of the network (SWD), those based on the average geodesic distance between nodes (SWA), and those based on the median geodesic distance (SWMd). These types of networks are defined as limiting properties of sequences of sets. We show the exact relation between these three types, namely that each SWD network is also an SWA network and that each SWA network is also an SWMd network. Yet, having the small-world property is a phenomenon that can easily occur in the sense that most networks are small-world networks in one of the three ways. We introduce sequences of distance frequencies, so-called alpha-sequences, and prove a relation between the majorization property between alpha-sequences and small-world properties.</p>","PeriodicalId":21755,"journal":{"name":"Scientometrics","volume":"1 1","pages":""},"PeriodicalIF":3.5000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Scientometrics","FirstCategoryId":"91","ListUrlMain":"https://doi.org/10.1007/s11192-024-05119-8","RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
We introduce and define three types of small worlds: small worlds based on the diameter of the network (SWD), those based on the average geodesic distance between nodes (SWA), and those based on the median geodesic distance (SWMd). These types of networks are defined as limiting properties of sequences of sets. We show the exact relation between these three types, namely that each SWD network is also an SWA network and that each SWA network is also an SWMd network. Yet, having the small-world property is a phenomenon that can easily occur in the sense that most networks are small-world networks in one of the three ways. We introduce sequences of distance frequencies, so-called alpha-sequences, and prove a relation between the majorization property between alpha-sequences and small-world properties.
期刊介绍：
Scientometrics aims at publishing original studies, short communications, preliminary reports, review papers, letters to the editor and book reviews on scientometrics. The topics covered are results of research concerned with the quantitative features and characteristics of science. Emphasis is placed on investigations in which the development and mechanism of science are studied by means of (statistical) mathematical methods.
The Journal also provides the reader with important up-to-date information about international meetings and events in scientometrics and related fields. Appropriate bibliographic compilations are published as a separate section. Due to its fully interdisciplinary character, Scientometrics is indispensable to research workers and research administrators throughout the world. It provides valuable assistance to librarians and documentalists in central scientific agencies, ministries, research institutes and laboratories.
Scientometrics includes the Journal of Research Communication Studies. Consequently its aims and scope cover that of the latter, namely, to bring the results of research investigations together in one place, in such a form that they will be of use not only to the investigators themselves but also to the entrepreneurs and research workers who form the object of these studies.
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