Emergence and size of the giant component in clustered random graphs with a given degree distribution Academic Article uri icon

abstract

  • Standard techniques for analyzing network models usually break down in the presence of clustering. Here we introduce a new analytic tool, the ``free-excess degree'' distribution, which extends the generating function framework, making it applicable for clustered networks ($C>0$). The methodology is general and provides a new expression for the threshold point at which the giant component emerges and shows that it scales as $(1\ensuremath{-}C{)}^{\ensuremath{-}1}$. In addition, the size of the giant component may be predicted even for more complicated scenarios such as the removal of a fixed fraction of nodes at random.

publication date

  • March 30, 2009