Cascades on clique-based graphs.

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.

Cascades on a class of clustered random networks.

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.

The unreasonable effectiveness of tree-based theory for networks with clustering.

We demonstrate that a tree-based theory for various dynamical processes operating on static, undirected networks yields extremely accurate results for several networks with high levels of clustering. We find that such a theory works well as long as the mean intervertex distance ℓ is sufficiently small--that is, as long as it is close to the value of ℓ in a random network with negligible clustering and the same degree-degree correlations. We support this hypothesis numerically using both real-world networks from various domains and several classes of synthetic clustered networks.

How clustering affects the bond percolation threshold in complex networks.

The question of how clustering (nonzero density of triangles) in networks affects their bond percolation threshold has important applications in a variety of disciplines. Recent advances in modeling highly clustered networks are employed here to analytically study the bond percolation threshold. In comparison to the threshold in an unclustered network with the same degree distribution and correlation structure, the presence of triangles in these model networks is shown to lead to a larger bond percolation threshold (i.