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Updated: May 31, 2026

Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations
Published on: February 15, 2017
Cascades on a class of clustered random networks
Adam Hackett1, Sergey Melnik, James P Gleeson
1MACSI, Department of Mathematics & Statistics, University of Limerick, Ireland.
Abstract:
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.
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