, Volume 80, Issue 11, pp 3397–3427 | Cite as

De-anonymization of Heterogeneous Random Graphs in Quasilinear Time

  • Karl Bringmann
  • Tobias Friedrich
  • Anton Krohmer


There are hundreds of online social networks with altogether billions of users. Many such networks publicly release structural information, with all personal information removed. Empirical studies have shown, however, that this provides a false sense of privacy—it is possible to identify almost all users that appear in two such anonymized network as long as a few initial mappings are known. We analyze this problem theoretically by reconciling two versions of an artificial power-law network arising from independent subsampling of vertices and edges. We present a new algorithm that identifies most vertices and makes no wrong identifications with high probability. The number of vertices matched is shown to be asymptotically optimal. For an n-vertex graph, our algorithm uses \(n^\varepsilon \) seed nodes (for an arbitrarily small \(\varepsilon \)) and runs in quasilinear time. This improves previous theoretical results which need \(\Theta (n)\) seed nodes and have runtimes of order \(n^{1+\Omega (1)}\). Additionally, the applicability of our algorithm is studied experimentally on different networks.


Social networks Locality-sensitive hashing Network privacy 



We thank Silvio Lattanzi from Google Inc. for fruitful discussions, sharing their data sets, and sending us a preliminary version of [18] at the early stages of this project. Karl Bringmann is a recipient of the Google Europe Fellowship in Randomized Algorithms, and this research is supported in part by this Google Fellowship. Tobias Friedrich received funding from the German Research Foundation (DFG) under Grant Agreement No. FR 2988 (ADLON).


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© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Max Planck Institute for InformaticsSaarbrückenGermany
  2. 2.Hasso Plattner InstitutePotsdamGermany

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