Phys. Rev. Lett. 102, 138701 (2009) [4 pages]Emergence and Size of the Giant Component in Clustered Random Graphs with a Given Degree DistributionReceived 26 September 2007; published 30 March 2009 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. © 2009 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.102.138701
DOI:
10.1103/PhysRevLett.102.138701
PACS:
89.75.Hc, 64.60.A−
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