IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v226y2013i2p354-365.html
   My bibliography  Save this article

Modeling centrality measures in social network analysis using bi-criteria network flow optimization problems

Author

Listed:
  • Gómez, Daniel
  • Figueira, José Rui
  • Eusébio, Augusto

Abstract

Centrality measures play an important role in the field of network analysis. In the particular case of social networks, the flow represents the way in which information passes through the network nodes. Freeman et al. (1991) were the first authors to relate centrality measures to network flow optimization problems in terms of betweenness, closeness, and the influence of one node over another one. Such measures are single dimensional and, in general, they amalgamate several heterogeneous dimensions into a single one, which is not suitable for dealing with most real-world problems. In this paper we extend the betweenness centrality measure (or concept) to take into account explicitly several dimensions (criteria). A new closeness centrality measure is defined to deal not only with the maximum flow between every ordered pair of nodes, but also with the cost associated with communications. We shall show how the classical measures can be enhanced when the problem is modeled as a bi-criteria network flow optimization problem.

Suggested Citation

  • Gómez, Daniel & Figueira, José Rui & Eusébio, Augusto, 2013. "Modeling centrality measures in social network analysis using bi-criteria network flow optimization problems," European Journal of Operational Research, Elsevier, vol. 226(2), pages 354-365.
    • Handle: RePEc:eee:ejores:v:226:y:2013:i:2:p:354-365
    DOI: 10.1016/j.ejor.2012.11.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712008752
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2012.11.027?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gert Sabidussi, 1966. "The centrality index of a graph," Psychometrika, Springer;The Psychometric Society, vol. 31(4), pages 581-603, December.
    2. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, December.
    3. Gomez, Daniel & Gonzalez-Aranguena, Enrique & Manuel, Conrado & Owen, Guillermo & del Pozo, Monica & Tejada, Juan, 2003. "Centrality and power in social networks: a game theoretic approach," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 27-54, August.
    4. Sohn, Keemin & Kim, Daehyun, 2010. "Zonal centrality measures and the neighborhood effect," Transportation Research Part A: Policy and Practice, Elsevier, vol. 44(9), pages 733-743, November.
    5. Alexander Erath & Michael Löchl & Kay Axhausen, 2009. "Graph-Theoretical Analysis of the Swiss Road and Railway Networks Over Time," Networks and Spatial Economics, Springer, vol. 9(3), pages 379-400, September.
    6. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer;The Psychometric Society, vol. 18(1), pages 39-43, March.
    7. Gómez, D. & González-Arangüena, E. & Manuel, C. & Owen, G., 2008. "A value for generalized probabilistic communication situations," European Journal of Operational Research, Elsevier, vol. 190(2), pages 539-556, October.
    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. Seema Rani & Monica Mehrotra, 2019. "Community Detection in Social Networks: Literature Review," Journal of Information & Knowledge Management (JIKM), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-28, June.
    2. Hyundong Nam & Taewoo Nam, 2021. "Exploring Strategic Directions of Pandemic Crisis Management: A Text Analysis of World Economic Forum COVID-19 Reports," Sustainability, MDPI, vol. 13(8), pages 1-19, April.
    3. Arcagni, Alberto & Grassi, Rosanna & Stefani, Silvana & Torriero, Anna, 2017. "Higher order assortativity in complex networks," European Journal of Operational Research, Elsevier, vol. 262(2), pages 708-719.
    4. Vidal-Tomás, David, 2021. "Transitions in the cryptocurrency market during the COVID-19 pandemic: A network analysis," Finance Research Letters, Elsevier, vol. 43(C).
    5. Sotaro Shibayama & Jian Wang, 2020. "Measuring originality in science," Scientometrics, Springer;Akadémiai Kiadó, vol. 122(1), pages 409-427, January.
    6. Rusinowska, Agnieszka & Taalaibekova, Akylai, 2019. "Opinion formation and targeting when persuaders have extreme and centrist opinions," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 9-27.
    7. Alessandro Avenali, 2014. "Relationships between centrality measures and VCG mechanism," DIAG Technical Reports 2014-05, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    8. Bekiros, Stelios & Nguyen, Duc Khuong & Sandoval Junior, Leonidas & Uddin, Gazi Salah, 2017. "Information diffusion, cluster formation and entropy-based network dynamics in equity and commodity markets," European Journal of Operational Research, Elsevier, vol. 256(3), pages 945-961.
    9. Castro, Jordi & Nasini, Stefano, 2015. "Mathematical programming approaches for classes of random network problems," European Journal of Operational Research, Elsevier, vol. 245(2), pages 402-414.
    10. Manuel, Paul & Brešar, Boštjan & Klavžar, Sandi, 2022. "The geodesic-transversal problem," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    11. Ballings, Michel & Van den Poel, Dirk, 2015. "CRM in social media: Predicting increases in Facebook usage frequency," European Journal of Operational Research, Elsevier, vol. 244(1), pages 248-260.
    12. Chabot, Miia & Bertrand, Jean-Louis, 2021. "Complexity, interconnectedness and stability: New perspectives applied to the European banking system," Journal of Business Research, Elsevier, vol. 129(C), pages 784-800.
    13. Simon de Blas, Clara & Simon Martin, Jose & Gomez Gonzalez, Daniel, 2018. "Combined social networks and data envelopment analysis for ranking," European Journal of Operational Research, Elsevier, vol. 266(3), pages 990-999.
    14. Fei, Liguo & Deng, Yong, 2017. "A new method to identify influential nodes based on relative entropy," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 257-267.
    15. Carlo Drago & Roberto Ricciuti, 2019. "Bootstrapping the Gini Index of the Network Degree: An Application for Italian Corporate Governance," Working Papers 05/2019, University of Verona, Department of Economics.
    16. Clara Simon de Blas & Daniel Gomez Gonzalez & Regino Criado Herrero, 2021. "Network analysis: An indispensable tool for curricula design. A real case-study of the degree on mathematics at the URJC in Spain," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-21, March.
    17. Koopo Kwon & Sungchan Jun & Yong-Jae Lee & Sanghei Choi & Chulung Lee, 2022. "Logistics Technology Forecasting Framework Using Patent Analysis for Technology Roadmap," Sustainability, MDPI, vol. 14(9), pages 1-30, April.
    18. Xian Cheng & Shaoyi Liao & Zhongsheng Hua, 2017. "A policy of picking up parcels for express courier service in dynamic environments," International Journal of Production Research, Taylor & Francis Journals, vol. 55(9), pages 2470-2488, May.
    19. Rysz, Maciej & Mahdavi Pajouh, Foad & Pasiliao, Eduardo L., 2018. "Finding clique clusters with the highest betweenness centrality," European Journal of Operational Research, Elsevier, vol. 271(1), pages 155-164.
    20. Wane, Abdrahmane & Touré, Ibra & Mballo, Aliou Diouf & Nokho, Cheikh Ibrahima & Ndiaye Aminata Konaté, 2017. "Non-livestock value chains. Lateral thinking for the securing of the Sahelian livestock economies," Bio-based and Applied Economics Journal, Italian Association of Agricultural and Applied Economics (AIEAA), vol. 6(2), September.
    21. Daniel Gómez & Javier Castro & Inmaculada Gutiérrez & Rosa Espínola, 2021. "A New Edge Betweenness Measure Using a Game Theoretical Approach: An Application to Hierarchical Community Detection," Mathematics, MDPI, vol. 9(21), pages 1-29, October.
    22. Ali Tosyali & Jeongsub Choi & Byunghoon Kim & Hoshin Lee & Myong K. Jeong, 2021. "A dynamic graph-based approach to ranking firms for identifying key players using inter-firm transactions," Annals of Operations Research, Springer, vol. 303(1), pages 5-27, August.

    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. René van den Brink & Agnieszka Rusinowska, 2017. "The degree measure as utility function over positions in networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01592181, HAL.
    2. van den Brink, René & Rusinowska, Agnieszka, 2022. "The degree measure as utility function over positions in graphs and digraphs," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1033-1044.
    3. C. Manuel & D. Martín, 2021. "A value for communication situations with players having different bargaining abilities," Annals of Operations Research, Springer, vol. 301(1), pages 161-182, June.
    4. Umed Temurshoev, 2008. "Who's Who in Networks. Wanted: the Key Group," Working Papers 08-08, NET Institute, revised Sep 2008.
    5. Yu, Senbin & Gao, Liang & Xu, Lida & Gao, Zi-You, 2019. "Identifying influential spreaders based on indirect spreading in neighborhood," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 418-425.
    6. Wang, Zhixiao & Zhao, Ya & Xi, Jingke & Du, Changjiang, 2016. "Fast ranking influential nodes in complex networks using a k-shell iteration factor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 171-181.
    7. Belik, Ivan & Jörnsten, Kurt, 2015. "The Analysis of Leadership Formation in Networks Based on Shapley Value," Discussion Papers 2015/2, Norwegian School of Economics, Department of Business and Management Science.
    8. Xu, Xiao-Ke & Wang, Xue & Xiao, Jing, 2018. "Inferring parent–child relationships by a node-remove centrality framework in online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 222-232.
    9. Li, Yongli & Wu, Chong & Wang, Xiaoyu & Luo, Peng, 2014. "A network-based and multi-parameter model for finding influential authors," Journal of Informetrics, Elsevier, vol. 8(3), pages 791-799.
    10. Belik, Ivan & Jörnsten, Kurt, 2016. "The method of leader's overthrow in networks based on Shapley value," Socio-Economic Planning Sciences, Elsevier, vol. 56(C), pages 55-66.
    11. 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.
    12. René van den Brink & Agnieszka Rusinowska, 2023. "Degree Centrality, von Neumann-Morgenstern Expected Utility and Externalities in Networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-04188289, HAL.
    13. Zhang, Xiaohang & Cui, Huiyuan & Zhu, Ji & Du, Yu & Wang, Qi & Shi, Wenhua, 2017. "Measuring the dissimilarity of multiplex networks: An empirical study of international trade networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 380-394.
    14. Enrique González-Arangüena & Conrado Manuel & Daniel Gomez & René van den Brink, 2008. "A Value for Directed Communication Situations," Tinbergen Institute Discussion Papers 08-006/1, Tinbergen Institute.
    15. David L. Alderson & Daniel Funk & Ralucca Gera, 2020. "Analysis of the global maritime transportation system as a layered network," Journal of Transportation Security, Springer, vol. 13(3), pages 291-325, December.
    16. Yeruva, Sujatha & Devi, T. & Reddy, Y. Samtha, 2016. "Selection of influential spreaders in complex networks using Pareto Shell decomposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 133-144.
    17. Francis Bloch & Matthew O. Jackson & Pietro Tebaldi, 2023. "Centrality measures in networks," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(2), pages 413-453, August.
    18. Marco Pelliccia, 2012. "Risk-sharing and probabilistic network structure," Birkbeck Working Papers in Economics and Finance 1214, Birkbeck, Department of Economics, Mathematics & Statistics.
    19. González–Arangüena, E. & Manuel, C. & Owen, G. & del Pozo, M., 2017. "The within groups and the between groups Myerson values," European Journal of Operational Research, Elsevier, vol. 257(2), pages 586-600.
    20. Wu, Tao & Xian, Xingping & Zhong, Linfeng & Xiong, Xi & Stanley, H. Eugene, 2018. "Power iteration ranking via hybrid diffusion for vital nodes identification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 802-815.

    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:eee:ejores:v:226:y:2013:i:2:p:354-365. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.