Preventing Unraveling in Social Networks: The Anchored k-Core Problem

  • Kshipra Bhawalkar
  • Jon Kleinberg
  • Kevin Lewi
  • Tim Roughgarden
  • Aneesh Sharma
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7392)


We consider a model of user engagement in social networks, where each player incurs a cost to remain engaged but derives a benefit proportional to the number of engaged neighbors. The natural equilibrium of this model corresponds to the k-core of the social network — the maximal induced subgraph with minimum degree at least k.

We study the problem of “anchoring” a small number of vertices to maximize the size of the corresponding anchored k-core — the maximal induced subgraph in which every non-anchored vertex has degree at least k. This problem corresponds to preventing “unraveling” — a cascade of iterated withdrawals. We provide polynomial-time algorithms for general graphs with k = 2, and for bounded-treewidth graphs with arbitrary k. We prove strong inapproximability results for general graphs and k ≥ 3.


Social Network General Graph Tree Decomposition Full Version Pure Nash Equilibrium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Kshipra Bhawalkar
    • 1
  • Jon Kleinberg
    • 2
  • Kevin Lewi
    • 1
  • Tim Roughgarden
    • 1
  • Aneesh Sharma
    • 3
  1. 1.Stanford UniversityStanfordUSA
  2. 2.Cornell UniversityIthacaUSA
  3. 3.Twitter, Inc.USA

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