Watching TV in UK I came across a commercial with Kevin Bacon making fun of his many connections. What started as a game (see here for a thorough explanation), made the theory of complex networks known for the general public. The Bacon number is the lower number of links an actor has with Kevin Bacon. For example, if an actor (or actress) played a role in the same film Bacon did, he or she has Bacon number 1. If he or she played a role with somebody who directly played with Kevin Bacon, he/she has Bacon number 2, and so on. Of course, Bacon has 0 as his Bacon number. You can check the Bacon number for all the actors and actresses in the Internet Movie Database (IMDb) in The Oracle of Bacon. It is striking to see that the higher number is only 9. So, it seems that everybody is very closely linked to Kevin Bacon. Thus the joke of he being the center of the Universe.

This concept is similar to the 6 degrees of separation popularized by the experiment of Milgram. This experiment was like this: you pick two people at random in the world (Milgram did it for the USA), and send a parcel to one of them, telling them that he or she has to reach the other person by direct links, sending the parcel to a known person that could be 'closer' (who knew the other person, or somebody who could know them) to the final receiver. He discovered that, in average, there were only 6 links of separation between sender and receiver. He called that the 'Small world' phenomenon.

This closeness between the individuals in the world can also be seen in the natural world. The trophic chains, cellular biology, evolutionary relationships, internet, scientific citation networks, even seismicity (I have published some papers on this particular field). In complex networks, the most important concept is not the individual, but the nature of its relationship with the other individuals.

Complex networks studies are based on the mathematical graph theory. And graph theory started as a game too, proposed by the eminent mathematician Leonhard Euler: can you find a path that crosses all the Bridges of Königsberg only once? Euler solved it inventing graph theory in the process.

It is important to analyze the relationships in a network. For example, it tells you who eats who in a trophic chain, or the main hubs in the internet. Why redundancy is important in the networks, so that a specific attack does not destroy the whole system. And many other applications. You can look it up in the internet, another network. Who said that playing games is not productive?

As a curiosity, in the scientific publication network (who published with whom) the center of the Universe is Erdős. Even some people has Erdős-Bacon number!

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