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Business & Information Systems Engineering
Erschienen in: Business & Information Systems Engineering 6/2010

01.12.2010 | State of the Art

A Critical Review of Centrality Measures in Social Networks

verfasst von: Dipl.-Math. oec., M.Sc. Andrea Landherr, Dipl.-Math. Bettina Friedl, Dr. Julia Heidemann

Erschienen in: Business & Information Systems Engineering | Ausgabe 6/2010

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Abstract

Social networks are currently gaining increasing impact in the light of the ongoing growth of web-based services like facebook.com. One major challenge for the economically successful implementation of selected management activities such as viral marketing is the identification of key persons with an outstanding structural position within the network. For this purpose, social network analysis provides a lot of measures for quantifying a member’s interconnectedness within social networks. In this context, our paper shows the state of the art with regard to centrality measures for social networks. Due to strongly differing results with respect to the quality of different centrality measures, this paper also aims at illustrating the tremendous importance of a reflected utilization of existing centrality measures. For this purpose, the paper analyzes five centrality measures commonly discussed in literature on the basis of three simple requirements for the behavior of centrality measures.
Vorheriger Artikel IT Governance and Types of IT Decision Makers in German Hospitals
Nächster Artikel Design Theory

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Fußnoten
1
If an approximation rather than a precise calculation of the values of BC is sufficient, the faster algorithm of Bader et al. (2007) can be used.
 
2
An automorphism is an isomorphism of a graph to itself, with two graphs G=(V G ,E G ) and G′=(V G′,E G′) being referred to as isomorphic if a bijection η:V G →V G′ exists with (a,b)∈E G if and only if (η(a),η(b))∈E G′ for all a, b∈V G .
 
3
An exception is the case that the new edge (x,y) is added and d G′(x,y)=1 results.
 
4
Being a non-negative, irreducible matrix, A always has a positive eigenvalue, which is equal to the spectral radius, and an associated eigenvector with only positive entries (Graham 1987, p. 131).
 
5
For detailed calculations and further details, see Appendix A.
 
6
In contrast to the work of Katz we abstain from normalizing the column sum of the adjacency matrix by multiplication with 1/(n−1). As a consequence, the result differs by a multiplicative constant from the outcome in the original work by Katz. In addition, under the assumptions described here, the CM by Katz differs only by a constant of the alpha centrality. Further details are outlined in Appendix B.
 
7
For detailed descriptions, see Appendix C.
 
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Metadaten
Titel
A Critical Review of Centrality Measures in Social Networks
verfasst von
Dipl.-Math. oec., M.Sc. Andrea Landherr
Dipl.-Math. Bettina Friedl
Dr. Julia Heidemann
Publikationsdatum
01.12.2010
Verlag
SP Gabler Verlag
Erschienen in
Business & Information Systems Engineering / Ausgabe 6/2010
Print ISSN: 2363-7005
Elektronische ISSN: 1867-0202
DOI
https://doi.org/10.1007/s12599-010-0127-3

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