Referee Reports for the Watts–Strogatz 'Small World' Paper

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Steve Strogatz posted his referee reports (with annotations for their revision plans) about his genre-defining 1998 ‘small world’ paper with Duncan Watts.

It just goes to show that misguided, skeptical reports (see Referee 2 in the upper right) happen to the best of us.

Referee 2 was confused about the implications of the work to systems other than those studied (and possibly even to those applications)…

(The source is Steve's tweet. I posted the picture separately to orient it correctly.)

It's a Small World After All: Part N

A very cool "small world" vignette from my current trip: One of the people who has attended many of my lectures at University of Costa Rica (10 hours in 3 days, and then 1 more hour today at a different campus) is a computer science professor whose sister is my Oxford mathematics colleague Xenia de la Ossa (with whom I have worked extensively for our recently-born masters program in mathematical and theoretical physics).

Academics are spread around the world and we get to travel to many interesting and diverse places, and it's simultaneously a small world. Both of these are great things.

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.

Finding a Lost Camera using the Small World Phenomenon

I wasn't following this story about the Facebook-mediated search for somebody's lost camera, but this is really cool for those of us who study network science. It's the small-world effect at work, with Facebook lending a helping hand. In fact, it's an absolutely beautiful example of cascading dynamics on small-world networks, and it might even be worth a mention in a paper on which I'm currently working on cascading dynamics on such networks (where my Facebook data is one of the many data sets we're employing).

It's also quite a nice story, as it's excellent that somebody would start such an effort for a total stranger. I hope that I'm eventually that nice a person. I'm rather good (I think) about caring about friends, but I do much less well about caring about people more generally.

(Tip of the cap to Martin Gould.)