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

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Vol. 83; no. 3 Pt 2; p. 036112
• Main Authors: Melnik, Sergey, Hackett, Adam, Porter, Mason A, Mucha, Peter J, Gleeson, James P
• Format: Journal Article
• Language: English
• Published: United States 01.03.2011
• ISSN: 1550-2376
• DOI: 10.1103/PhysRevE.83.036112

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.