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Centers in Connected Undirected Graphs: An Axiomatic Approach

Author

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  • Herman Monsuur

    (Royal Netherlands Naval College, Department of International Security Studies, P.O. Box 10.000, 1780 CA Den Helder, The Netherlands)

  • Ton Storcken

    (University of Maastricht, Department of Quantitative Methods, P.O. Box 616, 6200 MD Maastricht, The Netherlands)

Abstract

A center is a function that associates with every finite connected and undirected graph a nonempty subset of its vertices. These functions play an important role in networks such as social or interorganizational networks. Centers capture notions like: being a focal point of communication, being strategically located, ability and willingness to participate in strategic alliances, and the like. We focus on the conceptual issue of what makes a position in a graph a central one and investigate some possible concepts of centrality in relation to various properties. Characterizations of the uncovered center, the median, and degree center are presented, where each of these centers is defined for arbitrary connected undirected simple, and possibly cyclic, graphs.

Suggested Citation

  • Herman Monsuur & Ton Storcken, 2004. "Centers in Connected Undirected Graphs: An Axiomatic Approach," Operations Research, INFORMS, vol. 52(1), pages 54-64, February.
    • Handle: RePEc:inm:oropre:v:52:y:2004:i:1:p:54-64
    DOI: 10.1287/opre.1030.0082
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    References listed on IDEAS

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    1. Gert Sabidussi, 1966. "The centrality index of a graph," Psychometrika, Springer;The Psychometric Society, vol. 31(4), pages 581-603, December.
    2. Robert Delver & Herman Monsuur, 2001. "Stable sets and standards of behaviour," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 555-570.
    3. Ron Holzman, 1990. "An Axiomatic Approach to Location on Networks," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 553-563, August.
    4. Vohra, Rakesh, 1996. "An axiomatic characterization of some locations in trees," European Journal of Operational Research, Elsevier, vol. 90(1), pages 78-84, April.
    5. Bhaskar Dutta & Jean-Francois Laslier, 1999. "Comparison functions and choice correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 513-532.
    6. Dean P. Foster & Rakesh V. Vohra, 1998. "An Axiomatic Characterization of a Class of Locations in Tree Networks," Operations Research, INFORMS, vol. 46(3), pages 347-354, June.
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    Cited by:

    1. Khansa, Lara & Liginlal, Divakaran, 2012. "Whither information security? Examining the complementarities and substitutive effects among IT and information security firms," International Journal of Information Management, Elsevier, vol. 32(3), pages 271-281.
    2. László Csató, 2017. "Measuring centrality by a generalization of degree," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(4), pages 771-790, December.
    3. Janssen, R.H.P. & Monsuur, H., 2012. "Stable network topologies using the notion of covering," European Journal of Operational Research, Elsevier, vol. 218(3), pages 755-763.
    4. Monsuur, Herman, 2005. "Characterizations of the 3-cycle count and backward length of a tournament," European Journal of Operational Research, Elsevier, vol. 164(3), pages 778-784, August.
    5. Janssen, R.H.P. & Monsuur, H., 2013. "Identifying stable network structures and sets of key players using a W-covering perspective," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 245-253.

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