Category Archives: Complex Networks

Complex Networks

My Erdos Number is 4

Related to my previous post, I now have an Erdős number of 4. Another thing I’ve always wanted! Here are the details and an explanation of Erdős numbers for those who aren’t familiar with them.

I’ve posted previously about the mathematician Paul Erdős. Among other things, Erdős was insanely prolific and published 1,475 papers with 511 collaborators. Since one of his many areas of interest was graphs, it’s not surprising that a collaboration graph of his co-authors, and their co-authors, and so on…should be of interest. Courtesy of Wikipedia:

The Erdős number…describes the “collaborative distance” between a person and mathematician Paul Erdős, as measured by authorship of mathematical papers. It was created by friends as a humorous tribute to the enormous output of Erdős, one of the most prolific modern writers of mathematical papers, and has become well-known in scientific circles as a tongue-in-cheek measurement of mathematical prominence.

The Erdős collaboration graph is too huge to visualize, sadly, but the Erdős Number Project site has some interesting facts about the graph. Unfortunately, I think this information is skewed because it is based only on papers published in mathematical journals, while the high degree of interdisciplinary collaboration means that many people outside of mathematics have finite Erdős numbers. Anyway, according to this information, about 83,642 other people have Erdős number 4 (probably a gross underestimate.)

My relationship to Erdős comes from the fact that one of my co-authors, Michael Brudno, was a collaborator with at least two authors with Erdős number 2: Serafim Batzoglou and Lior Pachter. Each of those authors is a co-author with Daniel J. Kleitman, who not only has Erdős number 1, but has the lowest known Erdős-Bacon number: 3.

It’s conceivable that through one of Mike Brudno’s other collaborators, his number could in fact be 2, making mine 3, but confirming or disconfirming that would be too laborious. I’m more than satisfied with 4, which is slightly lower than the mean–especially considering that I never dreamed I’d have an Erdős number at all!

The Structure of Your Social Network

LinkedIn is the only “social networking” site I use. What it doesn’t have that I really want is a visual map of the structure of my social network. The structure of social networks in general is a hot research topic*. But I want to see what my social network actually looks like. Preferably out to 3 degrees of separation, with first and second degree nodes labelled with names (and links, natch.) It’s not enough to know who has lots of connections; I want to know with whom I have a high number of shared connections, i.e. who is a hub in my personal network. I also want to see the clusters that form in my own network. Some of these may be surprising, especially if 3rd degree links are included.

The real questions are: 1) is this something anyone else really cares about, and 2) is this something that LinkedIn would be loathe to provide—just as Google gives up zero information about link topology with its search results, presumably quite on purpose?

I could no doubt construct such a visualization myself, but given the way LinkedIn is set up it would have to involve a lot of yucky screen-scraping. Do any other “social networking” sites do a better job of coughing up real data on the structure of your personal network? If not, are they doing anything useful with this information themselves? I suspect not, which is just such a waste.

Network Visualization

I mentioned to someone the other day that I was a visualization junkie (long-time readers of may have noticed). Coincidentally I discovered a site that catalogs visualizations of complex networks: What’s nice is that you can suggest projects to add to the existing database, so this resource should continue to grow and remain fresh over time. Another current favourite is information aesthetics, a frequently updated blog highlighting information visualization in general, with many examples of networks. These are more than just eye candy, but it doesn’t hurt that the pictures are pretty.