Message-Passing Methods for Complex Contagions

  • James P. GleesonEmail author
  • Mason A. Porter
Part of the Computational Social Sciences book series (CSS)


Message-passing methods provide a powerful approach for calculating the expected size of cascades either on random networks (e.g., drawn from a configuration-model ensemble or its generalizations) asymptotically as the number N of nodes becomes infinite or on specific finite-size networks. We review the message-passing approach and show how to derive it for configuration-model networks using the methods of Gleeson and Cahalane (Phys Rev E 75(5):056103, 2007), Gleeson (Phys Rev E 77(4):046117, 2008), and Dhar et al. (J Phys A Math Gen 30(15):5259, 1997). Using this approach, we explain for such networks how to determine an analytical expression for a “cascade condition,” which determines whether a global cascade will occur. We extend this approach to message-passing methods for specific finite-size networks, and we derive a generalized cascade condition. Throughout this chapter, we illustrate these ideas using the Watts threshold model.



This work was supported by Science Foundation Ireland on grants that were awarded to JPG (grant numbers 16/IA/4470 and 11/PI/1026). We acknowledge the SFI/HEA Irish Centre for High-End Computing (ICHEC) for the provision of computational facilities.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.MACSI, Department of Mathematics and StatisticsUniversity of LimerickLimerickIreland
  2. 2.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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