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Re-conceptualizing centrality in social networks†

Published online by Cambridge University Press:  26 September 2016

D. SCHOCH  and
U. BRANDES
D. SCHOCH
Affiliation:
Departement of Computer & Information Science, University of Konstanz, Konstanz, Germany emails: [email protected], [email protected] Graduate School of Decision Sciences, University of Konstanz, Konstanz, Germany
U. BRANDES
Affiliation:
Departement of Computer & Information Science, University of Konstanz, Konstanz, Germany emails: [email protected], [email protected] Graduate School of Decision Sciences, University of Konstanz, Konstanz, Germany
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Abstract

In the social sciences, networks are used to represent relationships between social actors, be they individuals or aggregates. The structural importance of these actors is assessed in terms of centrality indices which are commonly defined as graph invariants. Many such indices have been proposed, but there is no unifying theory of centrality. Previous attempts at axiomatic characterization have been focused on particular indices, and the conceptual frameworks that have been proposed alternatively do not lend themselves to mathematical treatment.

We show that standard centrality indices, although seemingly distinct, can in fact be expressed in a common framework based on path algebras. Since, as a consequence, all of these indices preserve the neighbourhood-inclusion pre-order, the latter provides a conceptually clear criterion for the definition of centrality indices.

Keywords

network sciencesocial networkscentralityrankingpositional dominance
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Special Issue 6: Network Analysis and Modelling , December 2016 , pp. 971 - 985
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

†

We gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft under grant Br 2158/6-1. Part of this research was presented at the SIAM Workshop on Network Science (Snowbird, Utah, May 2015).

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