2009/03/30 by Yakir Berchenko, Yael Artzy‐Randrup, Mina Teicher +1 · 2 citations
Physics and Astronomy · Mathematics · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Graph theory and applications #Giant component #Component (thermodynamics) #Degree distribution #Degree (music) #Cluster analysis #Statistical physics #Fraction (chemistry) #Random graph #Function (biology) #Point (geometry) #Distribution (mathematics) #Computer science #Mathematics #Complex network #Combinatorics #Physics #Statistics #Theoretical computer science #Mathematical analysis #Geometry #Graph
paper · doi:10.1103/physrevlett.102.138701
openalex publication_date 2009/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02
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.