IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i6p939-d1610613.html
   My bibliography  Save this article

Generalized Closeness and Decay Stability of Some Graphs

Author

Listed:
  • Darja Rupnik Poklukar

    (The Faculty of Mechanical Engineering (FME), University of Ljubljana, Aškerčeva 6, 1000 Ljubljana, Slovenia
    These authors contributed equally to this work.)

  • Janez Žerovnik

    (The Faculty of Mechanical Engineering (FME), University of Ljubljana, Aškerčeva 6, 1000 Ljubljana, Slovenia
    Rudolfovo—Scientific and Technological Center Novo Mesto, Podbreznik 15, 8000 Novo Mesto, Slovenia
    These authors contributed equally to this work.)

Abstract

Generalized closeness is a recently defined centrality measure. Decay stability, based on generalized closeness, has been previously studied, leading to several conjectures on the decay stability of certain graph classes. In this work, we disprove two of these conjectures by showing that the Cartesian and strong products of paths are not decay stable.

Suggested Citation

  • Darja Rupnik Poklukar & Janez Žerovnik, 2025. "Generalized Closeness and Decay Stability of Some Graphs," Mathematics, MDPI, vol. 13(6), pages 1-9, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:939-:d:1610613
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/6/939/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/6/939/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer;The Psychometric Society, vol. 18(1), pages 39-43, March.
    2. Dangalchev, Chavdar, 2006. "Residual closeness in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(2), pages 556-564.
    Full references (including those not matched with items on IDEAS)

    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. Yelai Feng & Huaixi Wang & Chao Chang & Hongyi Lu, 2022. "Intrinsic Correlation with Betweenness Centrality and Distribution of Shortest Paths," Mathematics, MDPI, vol. 10(14), pages 1-18, July.
    2. Wang, Xiaojie & Su, Yanyuan & Zhao, Chengli & Yi, Dongyun, 2016. "Effective identification of multiple influential spreaders by DegreePunishment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 238-247.
    3. Liu, Xiaodong & Patacchini, Eleonora & Zenou, Yves & Lee, Lung-Fei, 2011. "Criminal Networks: Who is the Key Player?," Research Papers in Economics 2011:7, Stockholm University, Department of Economics.
    4. Gabrielle Demange, 2018. "Contagion in Financial Networks: A Threat Index," Management Science, INFORMS, vol. 64(2), pages 955-970, February.
    5. Fazal Hayat & Daniele Ettore Otera, 2024. "Maximizing Closeness in Bipartite Networks: A Graph-Theoretic Analysis," Mathematics, MDPI, vol. 12(13), pages 1-13, June.
    6. Lin, Dan & Wu, Jiajing & Xuan, Qi & Tse, Chi K., 2022. "Ethereum transaction tracking: Inferring evolution of transaction networks via link prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    7. Zhepeng Li & Xiao Fang & Xue Bai & Olivia R. Liu Sheng, 2017. "Utility-Based Link Recommendation for Online Social Networks," Management Science, INFORMS, vol. 63(6), pages 1938-1952, June.
    8. Dequiedt, Vianney & Zenou, Yves, 2017. "Local and consistent centrality measures in parameterized networks," Mathematical Social Sciences, Elsevier, vol. 88(C), pages 28-36.
    9. Colombo, Luca & Labrecciosa, Paola & Rusinowska, Agnieszka, 2025. "A dynamic analysis of criminal networks," Journal of Economic Theory, Elsevier, vol. 223(C).
    10. ,, 2014. "A ranking method based on handicaps," Theoretical Economics, Econometric Society, vol. 9(3), September.
    11. Ernest Liu & Aleh Tsyvinski, 2021. "Dynamical Structure and Spectral Properties of Input-Output Networks," Working Papers 2021-13, Princeton University. Economics Department..
    12. Bouveret, Géraldine & Mandel, Antoine, 2021. "Social interactions and the prophylaxis of SI epidemics on networks," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    13. Noah E. Friedkin & Karen S. Cook, 1990. "Peer Group Influence," Sociological Methods & Research, , vol. 19(1), pages 122-143, August.
    14. 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.
    15. Verdier, Thierry & Zenou, Yves, 2017. "The role of social networks in cultural assimilation," Journal of Urban Economics, Elsevier, vol. 97(C), pages 15-39.
    16. Elosegui, Pedro & Forte, Federico D. & Montes-Rojas, Gabriel, 2022. "Network structure and fragmentation of the Argentinean interbank markets," Latin American Journal of Central Banking (previously Monetaria), Elsevier, vol. 3(3).
    17. Karpf, Andreas & Mandel, Antoine & Battiston, Stefano, 2018. "Price and network dynamics in the European carbon market," Journal of Economic Behavior & Organization, Elsevier, vol. 153(C), pages 103-122.
    18. V. Kumar & Vikram Bhaskaran & Rohan Mirchandani & Milap Shah, 2013. "Practice Prize Winner ---Creating a Measurable Social Media Marketing Strategy: Increasing the Value and ROI of Intangibles and Tangibles for Hokey Pokey," Marketing Science, INFORMS, vol. 32(2), pages 194-212, March.
    19. Harkins, Andrew, 2020. "Network Comparative Statics," The Warwick Economics Research Paper Series (TWERPS) 1306, University of Warwick, Department of Economics.
    20. Bramoullé, Yann & Genicot, Garance, 2024. "Diffusion and targeting centrality," Journal of Economic Theory, Elsevier, vol. 222(C).

    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:gam:jmathe:v:13:y:2025:i:6:p:939-:d:1610613. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.