Cascades on a class of clustered random networks

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 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 which 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.

10 pages

References in corpus (7)

• Random graphs with clustering
• Sandpile on Scale-Free Networks
• Random graphs containing arbitrary distributions of subgraphs
• k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects
• Bond percolation on a class of clustered random networks
• Component sizes in networks with arbitrary degree distributions
• Propagation dynamics on networks featuring complex topologies

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