The Geometric Protean Model for On-Line Social Networks

  • Anthony Bonato
  • Jeannette Janssen
  • Pawel Prałat
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6516)


We introduce a new geometric, rank-based model for the link structure of on-line social networks (OSNs). In the geo-protean (GEO-P) model for OSNs nodes are identified with points in Euclidean space, and edges are stochastically generated by a mixture of the relative distance of nodes and a ranking function. With high probability, the GEO-P model generates graphs satisfying many observed properties of OSNs, such as power law degree distributions, the small world property, densification power law, and bad spectral expansion. We introduce the dimension of an OSN based on our model, and examine this new parameter using actual OSN data.


Degree Distribution Average Degree Ranking Function Link Structure Expansion Property 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Anthony Bonato
    • 1
  • Jeannette Janssen
    • 2
  • Pawel Prałat
    • 3
  1. 1.Department of MathematicsRyerson UniversityTorontoCanada
  2. 2.Department of Mathematics and StatisticsDalhousie UniversityHalifaxCanada
  3. 3.Department of MathematicsWest Virginia UniversityMorgantownUSA

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