Emergence and Size of the Giant Component in Clustered Random Graphs with a Given Degree Distribution

摘要

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.