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 sma...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2011-03, Vol.83 (3 Pt 2), p.036112-036112, Article 036112
Main Authors: Melnik, Sergey, Hackett, Adam, Porter, Mason A, Mucha, Peter J, Gleeson, James P
Format: Article
Language:English
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Summary: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.
ISSN:1539-3755
1550-2376
DOI:10.1103/PhysRevE.83.036112