Wednesday, March 23, 2011

THE Unreasonable Effectiveness of Tree-Based Theory for Networks with Clustering

After 7 (count 'em!) page proofs, my new paper has just officially appeared in Physical Review E.

The title (with "THE" actually written as "The") alludes to a very famous paper by Eugene Wigner. We're certainly not the first people to allude to that paper in a paper title, but we enjoyed doing it nonetheless. One of the arts in writing (and, indeed, it is something I enjoy very much) is to come up with a clever title for ones papers.

During the page proof stage (which was a comedy of errors on the part of the publishers), PRE tried to remove the "The" from the title because it's apparently their policy not to allow article titles to start with "The". However, we objected very strongly, it seems that they forgot about this by the time we were done with the proofing process. We were thus able to get our preferred title after all. :)

One of the really cool things about this paper, by the way, is that we found unexpected subtleties about something that most people in the field mistakenly thought were completely understood. The reality is that there are still some rather interesting and subtle myseries remaining. See the paper for more details.

Anyway, here are some more paper details

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

Authors: Sergey Melnik, Adam Hackett, Mason A. Porter, Peter J. Mucha, and James P. Gleeson

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 \ell is sufficiently small -- that is, 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 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.

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