A Dynamic Model for On-Line Social Networks

  • Anthony Bonato
  • Noor Hadi
  • Paul Horn
  • Paweł Prałat
  • Changping Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5427)


We present a deterministic model for on-line social networks based on transitivity and local knowledge in social interactions. In the Iterated Local Transitivity (ILT) model, at each time-step and for every existing node x, a new node appears which joins to the closed neighbour set of x. The ILT model provably satisfies a number of both local and global properties that were observed in real-world on-line social and other complex networks, such as a densification power law, decreasing average distance, and higher clustering than in random graphs with the same average degree. Experimental studies of social networks demonstrate poor expansion properties as a consequence of the existence of communities with low number of inter-community links. A spectral gap for both the adjacency and normalized Laplacian matrices is proved for graphs arising from the ILT model, thereby simulating such bad expansion properties.


Adjacency Matrix Random Graph Binary Sequence Wiener Index Expansion Property 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Anthony Bonato
    • 1
  • Noor Hadi
    • 2
  • Paul Horn
    • 3
  • Paweł Prałat
    • 4
  • Changping Wang
    • 1
  1. 1.Ryerson UniversityTorontoCanada
  2. 2.Wilfrid Laurier UniversityWaterlooCanada
  3. 3.University of CaliforniaSan DiegoUSA
  4. 4.Dalhousie UniversityHalifaxCanada

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