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Stable network topologies using the notion of covering

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  • Janssen, R.H.P.
  • Monsuur, H.
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    Abstract

    An alternative perspective to evaluate networks and network evolution is introduced, based on the notion of covering. For a particular node in a network covering captures the idea of being outperformed by another node in terms of, for example, visibility and possibility of information gathering. In this paper, we focus on networks where these subdued network positions do not exist. We call these networks stable. Within this set we identify the minimal stable networks, which frequently have a ‘bubble-like’ structure. Severing a link in such a network results in at least one of the nodes being covered. In a minimal stable network therefore all nodes cooperate to avoid that one of the nodes ends up in a subdued position. Our results can be applied to, for example, the design of (covert) communication networks and the dynamics of social and information networks.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0377221711010563
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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 218 (2012)
    Issue (Month): 3 ()
    Pages: 755-763

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    Handle: RePEc:eee:ejores:v:218:y:2012:i:3:p:755-763

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Graph theory; Network evolution; Information network; Degree distribution; Network centric operations;

    References

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    1. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    2. Sanjeev Goyal, 2007. "Introduction to Connections: An Introduction to the Economics of Networks
      [Connections: An Introduction to the Economics of Networks]
      ," Introductory Chapters, Princeton University Press.
    3. Matthew O. Jackson & Asher Wolinsky, 1994. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Monsuur, Herman, 2007. "Stable and emergent network topologies: A structural approach," European Journal of Operational Research, Elsevier, vol. 183(1), pages 432-441, November.
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    Cited by:
    1. Harmsen - van Hout, Marjolein J.W. & Herings, P. Jean-Jacques & Dellaert, Benedict G.C., 2010. "Communication Network Formation with Link Specificity and Value Transferability," FCN Working Papers 15/2010, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN), revised Mar 2011.
    2. 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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