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Stable network topologies using the notion of covering

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  • Janssen, R.H.P.
  • Monsuur, H.

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.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:218:y:2012:i:3:p:755-763
    DOI: 10.1016/j.ejor.2011.12.001
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    References listed on IDEAS

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    1. Sanjeev Goyal, 2007. "Introduction to Connections: An Introduction to the Economics of Networks," Introductory Chapters,in: Connections: An Introduction to the Economics of Networks Princeton University Press.
    2. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    3. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    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., 2013. "Communication network formation with link specificity and value transferability," European Journal of Operational Research, Elsevier, vol. 229(1), pages 199-211.
    2. Harmsen - van Hout, Marjolein J.W. & Dellaert, Benedict G.C. & Herings, P. Jean-Jacques, 2016. "Heuristic decision making in network linking," European Journal of Operational Research, Elsevier, vol. 251(1), pages 158-170.
    3. Olaizola, Norma & Valenciano, Federico, 2014. "Asymmetric flow networks," European Journal of Operational Research, Elsevier, vol. 237(2), pages 566-579.
      • Olaizola Ortega, María Norma & Valenciano Llovera, Federico, 2012. "Asymmetric flow networks," IKERLANAK Ikerlanak;2012-60, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    4. 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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