The life and self-reflections of a professional mathematician

Category: networks

Western States Power Grid

Below is a network representing  the topology of the Western States Power Grid of the United States. The size and color intensity reflect the “importance” of a certain node. I wish those big red dots would never shut down!

western_states_power_grid copyData compiled by D. Watts and S. Strogatz and are available online at the Mark Newman‘s webpage. Visualization is done via yEd.


How small is our small world today?

In 1967, Stanley Milgram of Harvard performed an ingenious experiment, demonstrating that, although our world is highly clustered, it is still very connected: everyone is on average approximatrely six handshakes away from any other person on the planet; six degrees of separation. It would be interesting to repeat Milgram’s experiment in our days. How small is our small world today? On the one hand, thanks to globalization, the world is becoming more and more interconnected. The average number of friends (what the last word means) of a randomly chosen person grows with time. On the other hand, the total population of the planet grows much faster than exponentially. What is happening with our world? Is it expanding or shrinking in the Milgram’s sense?

Academic Genealogy

I spent a couple of recent evening at the Mathematics Genealogy Project digging up my academic genealogy. According to the database, my full academic genealogical tree (which is not a tree in mathematical sense!) has 131 vertices and 150 edges. Below is a small portion of this graph. I have brilliant “genes” :)


Small World

My Erdös number is 5.

K. M. Zuev coauthored with A. V. Bolsinov paper
A. V. Bolsinov coauthored with V. I. Arnolʹd paper
V. I. Arnolʹd coauthored with Y. F. Meyer paper
Y. F. Meyer coauthored with S. Hartman paper
S. Hartman coauthored with P. Erdős paper