Some Typical Properties of the Spatial Preferred Attachment Model

  • Colin Cooper
  • Alan Frieze
  • Paweł Prałat
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7323)


We investigate a stochastic model for complex networks, based on a spatial embedding of the nodes, called the Spatial Preferred Attachment (SPA) model. In the SPA model, nodes have spheres of influence of varying size, and new nodes may only link to a node if they fall within its influence region. The spatial embedding of the nodes models the background knowledge or identity of the node, which influences its link environment. In this paper, we focus on the (directed) diameter, small separators, and the (weak) giant component of the model.


Random Graph Small Separator Giant Component Geometric Graph Small World Property 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Colin Cooper
    • 1
  • Alan Frieze
    • 2
  • Paweł Prałat
    • 3
  1. 1.Department of Computer ScienceKings College, University of LondonLondonUK
  2. 2.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghU.S.A
  3. 3.Department of MathematicsRyerson UniversityTorontoCanada

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