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On the influence maximization problem and the percolation phase transition

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  • Kolumbus, Yoav
  • Solomon, Sorin

Abstract

We analyze the problem of network influence maximization in the uniform independent cascade model: Given a network with N nodes and a probability p for a node to contaminate a neighbor, find a set of k initially contaminated nodes that maximizes the expected number of eventually contaminated nodes. This problem is of interest theoretically and for many applications in social networks. Unfortunately, it is a NP-hard problem. Using Percolation Theory, we show that in practice the problem is hard only in a vanishing neighborhood of a critical value p=pc. For p>pc there exists a “Giant Cluster” of order N, that is easily found in finite time. For p

Suggested Citation

  • Kolumbus, Yoav & Solomon, Sorin, 2021. "On the influence maximization problem and the percolation phase transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    • Handle: RePEc:eee:phsmap:v:573:y:2021:i:c:s0378437121002004
    DOI: 10.1016/j.physa.2021.125928
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    1. A. Barrat & M. Weigt, 2000. "On the properties of small-world network models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 13(3), pages 547-560, February.
    2. Solomon Sorin & Golo Natasa, 2013. "Minsky Financial Instability, Interscale Feedback, Percolation and Marshall–Walras Disequilibrium," Accounting, Economics, and Law: A Convivium, De Gruyter, vol. 3(3), pages 167-260, October.
    3. Pradeep Dubey & Rahul Garg & Bernard De Meyer, 2006. "Competing for Customers in a Social Network," Cowles Foundation Discussion Papers 1591, Cowles Foundation for Research in Economics, Yale University.
    4. Bernard de Meyer & Pradeep K. Dubey & Rahul Garg, 2006. "Competing for Customers in a Social Network: The Quasi-linear Case," Post-Print hal-00367866, HAL.
    5. Akbarpour, Mohammad & Malladi, Suraj & Saberi, Amin, 2018. "Just a Few Seeds More: Value of Network Information for Diffusion," Research Papers 3678, Stanford University, Graduate School of Business.
    6. Stauffer, D. & Jan, N., 2000. "Sharp peaks in the percolation model for stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 277(1), pages 215-219.
    7. Koen Frenken, 2006. "Technological innovation and complexity theory," Economics of Innovation and New Technology, Taylor & Francis Journals, vol. 15(2), pages 137-155.
    8. Goldenberg, J & Libai, B & Solomon, S & Jan, N & Stauffer, D, 2000. "Marketing percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 335-347.
    9. Flaviano Morone & Hernán A. Makse, 2015. "Influence maximization in complex networks through optimal percolation," Nature, Nature, vol. 524(7563), pages 65-68, August.
    10. Cohen, Reuven & Havlin, Shlomo, 2004. "Fractal dimensions of percolating networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 6-13.
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    Cited by:

    1. Kazemzadeh, Farzaneh & Safaei, Ali Asghar & Mirzarezaee, Mitra, 2022. "Influence maximization in social networks using effective community detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).

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