IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v392y2013i12p2807-2820.html

Percolation on shopping and cashback electronic commerce networks

Author

Listed:
  • Fu, Tao
  • Chen, Yini
  • Qin, Zhen
  • Guo, Liping

Abstract

Many realistic networks live in the form of multiple networks, including interacting networks and interdependent networks. Here we study percolation properties of a special kind of interacting networks, namely Shopping and Cashback Electronic Commerce Networks (SCECNs). We investigate two actual SCECNs to extract their structural properties, and develop a mathematical framework based on generating functions for analyzing directed interacting networks. Then we derive the necessary and sufficient condition for the absence of the system-wide giant in- and out- component, and propose arithmetic to calculate the corresponding structural measures in the sub-critical and supercritical regimes. We apply our mathematical framework and arithmetic to those two actual SCECNs to observe its accuracy, and give some explanations on the discrepancies. We show those structural measures based on our mathematical framework and arithmetic are useful to appraise the status of SCECNs. We also find that the supercritical regime of the whole network is maintained mainly by hyperlinks between different kinds of websites, while those hyperlinks between the same kinds of websites can only enlarge the sizes of in-components and out-components.

Suggested Citation

  • Fu, Tao & Chen, Yini & Qin, Zhen & Guo, Liping, 2013. "Percolation on shopping and cashback electronic commerce networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(12), pages 2807-2820.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:12:p:2807-2820
    DOI: 10.1016/j.physa.2013.02.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437113001799
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2013.02.018?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Sergey V. Buldyrev & Roni Parshani & Gerald Paul & H. Eugene Stanley & Shlomo Havlin, 2010. "Catastrophic cascade of failures in interdependent networks," Nature, Nature, vol. 464(7291), pages 1025-1028, April.
    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. Yin, Yong & Sa, Jiming & Liu, Qiong & Zhang, Chaoyong & Zhou, Jian, 2019. "Robustness analysis of partially interdependent networks with different coupling preferences and multicluster functional nodes in VCMS," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 189-195.
    2. María Teresa Ballestar & Pilar Grau-Carles & Jorge Sainz, 2019. "Predicting customer quality in e-commerce social networks: a machine learning approach," Review of Managerial Science, Springer, vol. 13(3), pages 589-603, June.
    3. Ballestar, María Teresa & Grau-Carles, Pilar & Sainz, Jorge, 2016. "Consumer behavior on cashback websites: Network strategies," Journal of Business Research, Elsevier, vol. 69(6), pages 2101-2107.
    4. Afonso Vieira, Valter & Agnihotri, Raj & de Almeida, Marcos Inácio Severo & Lopes, Evandro Luiz, 2022. "How cashback strategies yield financial benefits for retailers: The mediating role of consumers’ program loyalty," Journal of Business Research, Elsevier, vol. 141(C), pages 200-212.

    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. Bier, Vicki & Gutfraind, Alexander, 2019. "Risk analysis beyond vulnerability and resilience – characterizing the defensibility of critical systems," European Journal of Operational Research, Elsevier, vol. 276(2), pages 626-636.
    2. Wang, Wei & Cai, Meng & Zheng, Muhua, 2018. "Social contagions on correlated multiplex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 121-128.
    3. Chao Zhang & Jingjing Kong & Slobodan P Simonovic, 2018. "Modeling joint restoration strategies for interdependent infrastructure systems," PLOS ONE, Public Library of Science, vol. 13(4), pages 1-18, April.
    4. I. Bonamassa & B. Gross & J. Kertész & S. Havlin, 2025. "Hybrid universality classes of systemic cascades," Nature Communications, Nature, vol. 16(1), pages 1-10, December.
    5. Fang Zhou & Xiang He & Yongbo Yuan & Mingyuan Zhang, 2020. "Influence of Interlink Topology on Multilayer Network Robustness," Sustainability, MDPI, vol. 12(3), pages 1-19, February.
    6. Gianluca Pescaroli & David Alexander, 2016. "Critical infrastructure, panarchies and the vulnerability paths of cascading disasters," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 82(1), pages 175-192, May.
    7. Balint, T. & Lamperti, F. & Mandel, A. & Napoletano, M. & Roventini, A. & Sapio, A., 2017. "Complexity and the Economics of Climate Change: A Survey and a Look Forward," Ecological Economics, Elsevier, vol. 138(C), pages 252-265.
    8. Yu, Jianyong & Jiang, J.C. & Xiang, Leijun, 2017. "Group-based strategy diffusion in multiplex networks with weighted values," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 148-156.
    9. Gao, Yan-Li & Chen, Shi-Ming & Nie, Sen & Ma, Fei & Guan, Jun-Jie, 2018. "Robustness analysis of interdependent networks under multiple-attacking strategies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 495-504.
    10. Firuzbakht, Sina & Khansari, Mohammad, 2026. "The Fibonacci resilient network: Emergent resilience from a deterministic generative rule," Chaos, Solitons & Fractals, Elsevier, vol. 205(C).
    11. Gurami Tsitsiashvili, 2021. "Construction and Analysis of Queuing and Reliability Models Using Random Graphs," Mathematics, MDPI, vol. 9(19), pages 1-14, October.
    12. Wang, Chengjiang & Wang, Li & Wang, Juan & Sun, Shiwen & Xia, Chengyi, 2017. "Inferring the reputation enhances the cooperation in the public goods game on interdependent lattices," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 18-29.
    13. Youba Nait Belaid & Patrick Coudray & José Sanchez-Torres & Yi-Ping Fang & Zhiguo Zeng & Anne Barros, 2021. "Resilience Quantification of Smart Distribution Networks—A Bird’s Eye View Perspective," Energies, MDPI, vol. 14(10), pages 1-29, May.
    14. Chen, Lei & Yue, Dong & Dou, Chunxia, 2019. "Optimization on vulnerability analysis and redundancy protection in interdependent networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1216-1226.
    15. Guido Caldarelli & Matthieu Cristelli & Andrea Gabrielli & Luciano Pietronero & Antonio Scala & Andrea Tacchella, 2012. "A Network Analysis of Countries’ Export Flows: Firm Grounds for the Building Blocks of the Economy," PLOS ONE, Public Library of Science, vol. 7(10), pages 1-11, October.
    16. Tang, Liang & Jing, Ke & He, Jie & Stanley, H. Eugene, 2016. "Robustness of assembly supply chain networks by considering risk propagation and cascading failure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 459(C), pages 129-139.
    17. Hao, Yucheng & Jia, Limin & Zio, Enrico & Wang, Yanhui & He, Zhichao, 2024. "A network-based approach to improving robustness of a high-speed train by structure adjustment," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    18. Kai Gong & Jia-Jian Wu & Ying Liu & Qing Li & Run-Ran Liu & Ming Tang, 2019. "The Effective Healing Strategy against Localized Attacks on Interdependent Spatially Embedded Networks," Complexity, Hindawi, vol. 2019, pages 1-10, May.
    19. Ma, Jinlong & Zhao, Hongfei, 2024. "Evaluation and threshold-based mutual supervision promotes the evolution of cooperation on interdependent networks," Applied Mathematics and Computation, Elsevier, vol. 479(C).
    20. Wu, Yipeng & Chen, Zhilong & Zhao, Xudong & Gong, Huadong & Su, Xiaochao & Chen, Yicun, 2021. "Propagation model of cascading failure based on discrete dynamical system," Reliability Engineering and System Safety, Elsevier, vol. 209(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    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:eee:phsmap:v:392:y:2013:i:12:p:2807-2820. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.