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Positional Dominance: Concepts and Algorithms

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Algorithms and Discrete Applied Mathematics (CALDAM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10156))

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Abstract

Centrality indices assign values to the vertices of a graph such that vertices with higher values are considered more central. Triggered by a recent result on the preservation of the vicinal preorder in rankings obtained from common centrality indices, we review and extend notions of domination among vertices. These may serve as building blocks for new concepts of centrality that extend more directly, and more coherently, to more general types of data such as multilayer networks. We also give efficient algorithms to construct the associated partial rankings.

We gratefully acknowledge financial support from Deutsche Forschungsgemeinschaft (DFG) under grants Br 2158/6-1 and Br 2158/11-1.

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Notes

  1. 1.

    In the following we assume that \(\deg (v) \le \deg (w)\), since otherwise w cannot dominate v w.r.t. positional dominance.

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Authors and Affiliations

  1. Computer and Information Science, University of Konstanz, Konstanz, Germany

    Ulrik Brandes, Moritz Heine, Julian Müller & Mark Ortmann

Authors
  1. Ulrik Brandes
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  2. Moritz Heine
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  3. Julian Müller
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  4. Mark Ortmann
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Correspondence to Julian Müller .

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Editors and Affiliations

  1. University of Lethbridge, Lethbridge, Alberta, Canada

    Daya Gaur

  2. Indian Institute of Technology Madras, Chennai, India

    N.S. Narayanaswamy

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Brandes, U., Heine, M., Müller, J., Ortmann, M. (2017). Positional Dominance: Concepts and Algorithms. In: Gaur, D., Narayanaswamy, N. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2017. Lecture Notes in Computer Science(), vol 10156. Springer, Cham. https://doi.org/10.1007/978-3-319-53007-9_6

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  • DOI: https://doi.org/10.1007/978-3-319-53007-9_6

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