The small-world phenomenon: a model, explanations, characterizations, and examples

IF 3.5 3区 管理学 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Leo Egghe, Ronald Rousseau
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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.

Abstract Image

小世界现象:模型、解释、特征和实例
我们引入并定义了三种类型的小世界:基于网络直径(SWD)的小世界,基于节点间平均大地测量距离(SWA)的小世界,以及基于大地测量距离中值(SWMd)的小世界。这些类型的网络被定义为集合序列的极限属性。我们展示了这三类网络之间的确切关系,即每个 SWD 网络也是 SWA 网络,每个 SWA 网络也是 SWMd 网络。然而,具有小世界属性是一种很容易出现的现象,因为大多数网络都是这三种方式之一的小世界网络。我们引入了距离频率序列,即所谓的阿尔法序列,并证明了阿尔法序列之间的大化特性与小世界特性之间的关系。
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来源期刊
Scientometrics
Scientometrics 管理科学-计算机:跨学科应用
CiteScore
7.20
自引率
17.90%
发文量
351
审稿时长
1.5 months
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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