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

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posted on 2023-01-09, 14:28 authored by Sergey Melnik, Adam W. Hackett, Mason A Porter, Peter J Mucha, James GleesonJames Gleeson
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.

History

Publication

Physical Review E;83, 036112

Publisher

American Physical Society

Note

peer-reviewed

Other Funding information

SFI

Language

English

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  • MACSI - Mathematics Application Consortium for Science & Industry

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  • Mathematics & Statistics

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