Emergence and size of the giant component in clustered random graphs with a given degree distribution.
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.
Berchenko
Yakir
Y
Brain Research Center, Bar Ilan University, Ramat Gan, Israel.
Artzy-Randrup
Yael
Y
Teicher
Mina
M
Stone
Lewi
L
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