Cascades on a class of clustered random networks

TL;DR

This paper develops an analytical method to predict cascade sizes in clustered random networks, accounting for various dynamical models and network structures, with results validated against simulations.

Contribution

It introduces a general analytical framework for cascade analysis on clustered networks, including criteria for global cascades and effects of clustering.

Findings

Analytical conditions for global cascades are derived.

Clustering can either increase or decrease cascade size depending on the model.

Analytical results match well with numerical simulations.

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.