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Percolation on shopping and cashback electronic commerce networks

Author

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  • 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
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    References listed on IDEAS

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    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.
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    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. 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.
    3. 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.
    4. 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.

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