Relationships between centrality measures of networks with diameter 2

From an intuitive analysis of the betweeness of networks in which we detail its components (not only the basic definition of the betweeness as the number of short paths through a node), we propose a relationship between the betweeness, the degree and the clustering coefficient of a node in networks...

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Bibliographic Details
Published in:Physica A 2018-09, Vol.505, p.243-251
Main Authors: Benguigui, L., Porat, I.
Format: Article
Language:English
Subjects:
Betweeness
Centralities
Clustering coefficient
Networks
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Summary:From an intuitive analysis of the betweeness of networks in which we detail its components (not only the basic definition of the betweeness as the number of short paths through a node), we propose a relationship between the betweeness, the degree and the clustering coefficient of a node in networks with diameter 2. We verify the validity of this relationship on seven diameter 2 networks: the global migration network, the dual networks of the underground systems of Barcelona, Tokyo, London and three model networks. We show also that the dependence of the closeness with the degree is an exact linear relation with slope equal to −1. •There is a precise functional dependence of the closeness with the degree: it is a linear relation with slope equal to −1.•A new intuitive approach of the concept of betweeness based of three contributions to this centrality.•A relationship between the degree, the betweeness and the clustering coefficient.•These new relations were verified in seven diameter 2 networks.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2018.03.058