  We present an analytical approach to determining the expected cascade size in
a broad range of dynamical models on the class of highly-clustered random
graphs introduced by Gleeson [J. P. Gleeson, Phys. Rev. E 80, 036107 (2009)]. A
condition for the existence of global cascades is also derived. Applications of
this approach include analyses of percolation, and Watts's model. We show how
our techniques can be used to study the effects of in-group bias in cascades on
social networks.
