Data Mining and Knowledge Discovery

, Volume 29, Issue 2, pp 423–465 | Cite as

Inhibiting diffusion of complex contagions in social networks: theoretical and experimental results

  • Chris J. Kuhlman
  • V. S. Anil Kumar
  • Madhav V. Marathe
  • S. S. Ravi
  • Daniel J. Rosenkrantz


We consider the problem of inhibiting undesirable contagions (e.g. rumors, spread of mob behavior) in social networks. Much of the work in this context has been carried out under the 1-threshold model, where diffusion occurs when a node has just one neighbor with the contagion. We study the problem of inhibiting more complex contagions in social networks where nodes may have thresholds larger than 1. The goal is to minimize the propagation of the contagion by removing a small number of nodes (called critical nodes) from the network. We study several versions of this problem and prove that, in general, they cannot even be efficiently approximated to within any factor \(\rho \ge 1\), unless P = NP. We develop efficient and practical heuristics for these problems and carry out an experimental study of their performance on three well known social networks, namely epinions, wikipedia and slashdot. Our results show that these heuristics perform significantly better than five other known methods. We also establish an efficiently computable upper bound on the number of nodes to which a contagion can spread and evaluate this bound on many real and synthetic networks.


Complex contagions Blocking Social networks 



We thank the reviewers for their careful reading of the manuscript and their suggestions and comments. We thank our external collaborators and members of the Network Dynamics and Simulation Science Laboratory (NDSSL) for their suggestions and comments. This work has been partially supported by NSF HSD Grant SES-0729441, NSF PetaApps Grant OCI-0904844, NSF NETS 1201 Grant CNS-0831633, NSF NetSE Grant CNS-1011769, NSF SDCI 1202 Grant OCI-1032677, DTRA R&D Grant HDTRA1-09-1-0017, DTRA Grant HDTRA1-11-1-0016, DTRA 1203 CNIMS Contract HDTRA1-11-D-0016-0001, NIH MIDAS Grant 1205 2U01GM070694-09, NIH MIDAS Grant 3U01FM070694-09S1, NIH MIDAS Grant 2U01GM070694-09, and LLNL Fellowship SubB596713.


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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Chris J. Kuhlman
    • 1
  • V. S. Anil Kumar
    • 1
  • Madhav V. Marathe
    • 1
  • S. S. Ravi
    • 2
  • Daniel J. Rosenkrantz
    • 2
  1. 1.Virginia Bioinformatics Institute, Virginia TechBlacksburgUSA
  2. 2.Department of Computer ScienceUniversity at Albany–SUNYAlbanyUSA

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