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

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

2010-01-09

arxiv.org/abs/1001.1439v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages, 8 figures

Scientific paper

10.1103/PhysRevE.83.036112

We demonstrate that a tree-based theory for various dynamical processes 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 $\ell$ is sufficiently small - i.e., as long as it is close to the value of $\ell$ in a random network with negligible clustering and the same degree-degree correlations. We confirm this hypothesis numerically using real-world networks from various domains and on 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.

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