IDEAS home Printed from https://ideas.repec.org/p/tkk/dpaper/dp106.html
   My bibliography  Save this paper

Bonacich Network Measures as Minimum Norm Solutions

Author

Listed:
  • Salonen Hannu

    (Department of Economics, University of Turku)

Abstract

An undirected connected bimodal network has two Bonacich measures quantifying the centrality of the nodes. We show that the product of Bonacich measures of an undirected bimodal network may be viewed as a product measure that is nearest (w.r.t. Euclidean norm) to the matrix representing the network. A directed bimodal network has four Bonacich measures, two inflow and two outflow measures. Given directed strongly connected bimodal network and its Bonacich inflow (or outflow) measures, there is undirected bimodal network with the same Bonacich measures. So Bonacich measures of directed bimodal network can also be viewed as minimum norm solutions.

Suggested Citation

  • Salonen Hannu, 2016. "Bonacich Network Measures as Minimum Norm Solutions," Discussion Papers 106, Aboa Centre for Economics.
    • Handle: RePEc:tkk:dpaper:dp106
    as

    Download full text from publisher

    File URL: http://ace-economics.fi/kuvat/dp106.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Hannu Salonen, 2015. "Bonacich Measures as Equilibria in Network Models," Discussion Papers 100, Aboa Centre for Economics.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Demange, Gabrielle, 2017. "Mutual rankings," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 35-42.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Simpson Zhang & Mihaela van der Schaar, 2018. "Reputational Dynamics in Financial Networks During a Crisis," Working Papers 18-03, Office of Financial Research, US Department of the Treasury.
    2. Orlova, Olena, 2020. "Personal preferences in networks," Center for Mathematical Economics Working Papers 631, Center for Mathematical Economics, Bielefeld University.
    3. Dalmazzo, Alberto & Pin, Paolo & Scalise, Diego, 2014. "Communities and social inefficiency with heterogeneous groups," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 410-427.
    4. Yann Bramoullé & Habiba Djebbari & Bernard Fortin, 2020. "Peer Effects in Networks: A Survey," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 603-629, August.
    5. Kenju Kamei & Louis Putterman, 2018. "Reputation Transmission Without Benefit To The Reporter: A Behavioral Underpinning Of Markets In Experimental Focus," Economic Inquiry, Western Economic Association International, vol. 56(1), pages 158-172, January.
    6. Dequiedt, Vianney & Zenou, Yves, 2017. "Local and consistent centrality measures in parameterized networks," Mathematical Social Sciences, Elsevier, vol. 88(C), pages 28-36.
    7. Daron Acemoglu & Asuman Ozdaglar & Alireza Tahbaz-Salehi, 2015. "Networks, Shocks, and Systemic Risk," NBER Working Papers 20931, National Bureau of Economic Research, Inc.
    8. Yann Algan & Quoc-Anh Do & Nicolò Dalvit & Alexis Le Chapelain & Yves Zenou, 2015. "How Social Networks Shape Our Beliefs: A Natural Experiment among Future French Politicians," Working Papers hal-03459820, HAL.
    9. Russell Golman & Aditi Jain & Sonica Saraf, 2019. "Hipsters and the Cool: A Game Theoretic Analysis of Social Identity, Trends and Fads," Papers 1910.13385, arXiv.org.
    10. Chen, Ying-Ju & Zenou, Yves & Zhou, Junjie, 2022. "The impact of network topology and market structure on pricing," Journal of Economic Theory, Elsevier, vol. 204(C).
    11. Picard, Pierre M. & Zenou, Yves, 2015. "Urban Spatial Structure, Employment and Social Ties: European versus American Cities," IZA Discussion Papers 9166, Institute of Labor Economics (IZA).
    12. Bayer, Péter & Herings, P. Jean-Jacques & Peeters, Ronald, 2021. "Farsighted manipulation and exploitation in networks," Journal of Economic Theory, Elsevier, vol. 196(C).
    13. Jadbabaie, Ali & Kakhbod, Ali, 2019. "Optimal contracting in networks," Journal of Economic Theory, Elsevier, vol. 183(C), pages 1094-1153.
    14. Bulat Sanditov & Saurabh Arora, 2016. "Social network and private provision of public goods," Journal of Evolutionary Economics, Springer, vol. 26(1), pages 195-218, March.
    15. John Higgins & Tarun Sabarwal, 2023. "Control and spread of contagion in networks with global effects," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 25(6), pages 1149-1187, December.
    16. Yann Bramoullé & Christian Ghiglino, 2022. "Loss Aversion and Conspicuous Consumption in Networks," AMSE Working Papers 2206, Aix-Marseille School of Economics, France.
    17. Zenou, Yves, 2012. "Networks in Economics," CEPR Discussion Papers 9021, C.E.P.R. Discussion Papers.
    18. Michael D. König & Xiaodong Liu & Yves Zenou, 2019. "R&D Networks: Theory, Empirics, and Policy Implications," The Review of Economics and Statistics, MIT Press, vol. 101(3), pages 476-491, July.
    19. Andrea Galeotti & Benjamin Golub & Sanjeev Goyal, 2020. "Targeting Interventions in Networks," Econometrica, Econometric Society, vol. 88(6), pages 2445-2471, November.
    20. Verdier, Thierry & Zenou, Yves, 2017. "The role of social networks in cultural assimilation," Journal of Urban Economics, Elsevier, vol. 97(C), pages 15-39.

    More about this item

    Keywords

    networks; influence measures; impact factors;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tkk:dpaper:dp106. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Susmita Baulia (email available below). General contact details of provider: https://edirc.repec.org/data/tukkkfi.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.