2010/12/31 by Adam Hackett, Sergey Melnik, James P. Gleeson · 119 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Artificial intelligence #Cascade #Class (philosophy) #Cluster analysis #Combinatorics #Complex Network Analysis Techniques #Computer science #Engineering #Mathematics #Opinion Dynamics and Social Influence #Percolation (cognitive psychology) #Percolation threshold #Physics #Quantum mechanics #Random graph #Range (aeronautics) #Statistical physics #Statistics #Stochastic processes and statistical mechanics #cond-mat.stat-mech #cs.SI #physics.soc-ph
paper · pdf · doi:10.1103/physreve.83.056107
published in Physical Review E 83(5), 056107 (American Physical Society) · 10 pages
arxiv created 2011/04/05 · openalex publication_date 2011/05/10 · arxiv updated 2013/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of random networks with arbitrary degree distribution and nonzero clustering introduced previously in [M. E. J. Newman, Phys. Rev. Lett. 103, 058701 (2009)]. A condition for the existence of global cascades is derived as well as a general criterion that determines whether increasing the level of clustering will increase, or decrease, the expected cascade size. Applications, examples of which are provided, include site percolation, bond percolation, and Watts' threshold model; in all cases analytical results give excellent agreement with numerical simulations.