title: The unreasonable effectiveness of tree-based theory for networks with clustering.
abstract: 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. We present analytical calculations that further support our claim that tree-based theories can be accurate for clustered networks, provided that the networks are "sufficiently small" worlds.
authors.affiliation: Department of Mathematics and Statistics, University of Limerick, Ireland.
authors.forename: Sergey
authors.initials: S
authors.lastname: Melnik
authors.forename: Adam
authors.initials: A
authors.lastname: Hackett
authors.forename: Mason A
authors.initials: MA
authors.lastname: Porter
authors.forename: Peter J
authors.initials: PJ
authors.lastname: Mucha
authors.forename: James P
authors.initials: JP
authors.lastname: Gleeson