title: Emergence and size of the giant component in clustered random graphs with a given degree distribution.
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-C)(-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.
authors.affiliation: Brain Research Center, Bar Ilan University, Ramat Gan, Israel.
authors.forename: Yakir
authors.initials: Y
authors.lastname: Berchenko
authors.forename: Yael
authors.initials: Y
authors.lastname: Artzy-Randrup
authors.forename: Mina
authors.initials: M
authors.lastname: Teicher
authors.forename: Lewi
authors.initials: L
authors.lastname: Stone
mesh_terms: D000465:Algorithms; D001703:Biophysics / Q000379:methods*; D016000:Cluster Analysis; D003196:Computer Graphics; D003198:Computer Simulation; D008954:Models, Biological; D015233:Models, Statistical; D008962:Models, Theoretical; D016571:Neural Networks, Computer; D012984:Software