Monday, November 9, 2015

What is Your Erdos Number and Network Science

On Friday, October 30, UMass Amherst had the pleasure of hearing Professor Albert-László Barabasi of Northeastern University speak on Network Science: From Structure to Control

This was a talk not to be missed. The talk was co-hosted by several entities at UMass including the Computational Social Science Institute (CSSI) ( a great group of colleagues with whom I enjoy being affiliated with). Room 150 in the Computer Science building was packed for his talk with an audience from many schools and colleges on our beautiful campus. My doctoral student, Shivani Shukla, and I represented the Isenberg School. Professor David Jensen of Computer Science introduced our distinguished speaker.

We had hosted Barabasi at the Isenberg School back in 2006 when I was on sabbatical at the Radcliffe Institute at Harvard in our great UMass Amherst INFORMS Speaker Series (and what an amazing list of speakers we had that Spring 2006, which even included Braess of Braess paradox fame).

I had last seen  Albert-László at a Network Science conference at the Media Lab at MIT, a few years ago,  to which I brought my doctoral student (now a Professor), Min Yu.

Barabasi began his lecture (I would have blogged it sooner but last week I was blogging from the INFORMS conference in Philadelphia and I was swamped) by bringing up Paul Erdos, a fellow Hungarian. Erdos,  the renowned mathematician,  had over 500 collaborators (some say 509 and others 511 - I have not counted them).  Erdos traveled the world from collaborator to collaborator with a suitcase typically staying for about 5 days.

Identifying one's Erdos number has become quite the hobby among STEM (and some other) folks. One has an Erdos number of 1 if one was a direct collaborator of Erdos', a number of 2, if one co-authored with a co-author of Erdos', and so on. My Erdos number is 4, by way of Paul Dupuis, Ofer Zeitouni, and Persi Diaconis.

You may be more familiar with the  Bacon number (named after the actor Kevin Bacon who starred in the move, "Footloose." 

And, of course, some actually know their Erdos + Bacon number.  Barabasi mentioned that his Bacon number was actually lower than his Erdos number, since he had been in a movie with someone who was in a movie with so and so and so on who starred with Kevin Bacon.

Now, what does this all have to do with Network Science?

Erdos is known for the Erdos-Renyi model in graph theory, which describes random graphs or networks. The degree distribution of the World Wide Web is not Poisson but follows the power law. Essentially, there are a very large number of small connected nodes in such a network and a few that are very highly connected. The World Wide Web is like an airline network with hubs. The Internet is a scale-free network according to the famous paper by yes, Faloutsos, Faloutsos and Faloutsos, but there has been some discussion about this claim.

Barabasi emphasized in his talk that a few actors are "hubs" and metabolic and protein interaction networks, which have evolved over 4 billions of years, also have hubs.

He noted that in network science (his books are definitely worth reading and he is highly cited), it is not just a matter of connecting nodes but that nodes are also evolving dynamically. He spoke of the preferential attachment model and then asked the question of where robustness comes from. He spoke about the Internet being robust to random failures and also noted that hubs are important both in the spread of ideas and diseases, as well. He referred to Vespignani, whom I have had the pleasure of meeting through the I3P association, which is a consortium based at Dartmouth.

His recent research, has, among many fascinating topics, been focusing on control. Just think of a car with 6,000 components but essentially only 4 are needed to control it. He also mentioned Kalman of Kalman filtering fame.

He described an interesting study that he conducted in Hungary in an organization to identify who were the hubs and found the 2 or 3 most influential people, one being the custodian, who was like "gossip central."

His talk was delivered with his fantastic energy, dynamism, and sense of humor. He included videos in addition to many vivid photographs. If you did not love networks before his talk, you would have fallen in love with them during it.

I was also very lucky to be invited to join Barabasi and a few colleagues from economics, computer science, and sociology (Professor James Kitts, who is the Co-Director of CSSI with Professor David Jensen). I also brought my husband along since he, like Barabasi, has a PhD in physics.

The discussions at dinner were fabulous. I wish that the evening would not end. We talked about topics as wide ranging as identifying Nobel prize winners from co-authorship of papers; determining through the language in an abstract whether a scientific paper was written by a female or a male, and we even discussed the Braess paradox.  I keep on emphasizing the importance of including flows and economic behavior of decision-makers in network science. We also discussed the success of the first PhD program in Network Science, which he helped to establish at Northeastern University and a similar PhD at a university in Hungary that he is affiliated with and that the billionaire Soros is helping to fund. Yes, Soros is also Hungarian.

below are photos taken at the dinner that great Friday evening.
Thanks to Professor Barabasi for coming out to Amherst from Boston and for your brilliant lecture on Network Science!