Social-Affiliation Networks: Patterns and the SOAR Model

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11052)


Given a social-affiliation network – a friendship graph where users have many, binary attributes e.g., check-ins, page likes or group memberships – what rules do its structural properties such as edge or triangle counts follow, in relation to its attributes? More challengingly, how can we synthetically generate networks which provably satisfy those rules or patterns? Our work attempts to answer these closely-related questions in the context of the increasingly prevalent social-affiliation graphs. Our contributions are two-fold: (a) Patterns: we discover three new rules (power laws) in the properties of attribute-induced subgraphs, substructures which connect the friendship structure to affiliations; (b) Model: we propose SOAR– short for SOcial-Affiliation graphs via Recursion– a stochastic model based on recursion and self-similarity, to provably generate graphs obeying the observed patterns. Experiments show that: (i) the discovered rules are useful in detecting deviations as anomalies and (ii) SOAR is fast and scales linearly with network size, producing graphs with millions of edges and attributes in only a few seconds. Code related to this paper is available at:


Graph mining Attributes Patterns Anomalies Generator 



This material is based upon work supported by the National Science Foundation under Grants No. CNS-1314632, IIS-1408924 and by DARPA under award FA8750-17-2-0130. Any opinions, findings, conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation, or other funding parties. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation here on.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Computer ScienceCarnegie Mellon UniversityPittsburghUSA
  2. 2.School of Computer ScienceMcGill UniversityMontrealCanada

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