Hubs and Centers of Information

by Yaniv Altshuler

In order to understand the importance of small world networks and specifically – its relevance to computational social finance, let us first take a metaphoric detour and discuss film actor Kevin Bacon. After having played in numerous films, in an interview held in 1994 Bacon commented that he believed he had worked with every actor in Hollywood either directly, or through another single connecting actor. Shortly after this comment, an internet newsgroup bearing the title “Kevin Bacon in the Center of the Universe” appeared, discussing the validity of this declaration. Becoming somewhat of an urban legend, this theory had gained increasing popularity, resulting in numerous discussions, parodies and even a trivia game and a charity organization (founded by Kevin Bacon himself).

Studied deeply, it seems that although slightly exaggerated, Bacon’s comment was not very far from reality. In fact, Bacon had directly played with 2480 different actors, who in turn played with 254428 different other unique actors. Still, there are 817491 other actors that can only be reached from Bacon using a “chain” of length three, and 201635 actors that require a chain of length four. The number of actors who require a longer is only 15788. Calculating the average distance of a Hollywood actor from Kevin Bacon yields the surprisingly small number 2.981.

Kevin Bacon

Still, it turns out that Kevin Bacon is *not* the center of the universe after all, as there are other actors that possess a shorter average shortest path from the Hollywood community. Observing the top 100 actors of this list yields a strange heterogeneous mix actors coming from different genres and time periods. As an example, following is the top 20 actors, including their appropriate “average shortest path” number :

Dennis Hopper (2.743), Harvey Keitel (2.77), Donald Sutherland (2.771), Udo Kier (2.776), David Carradine (2.778), Max von Sydow (2.782), Rod Steiger (2.784), Michael Caine (2.789), Martin Sheen (2.797), Seymour Cassel (2.797), Christopher Lee (2.8), Christopher Plummer (2.8), Ben Gazzara (2.8), John Hurt (2.8), Malcolm McDowell (2.8), Karen Black (2.8), Elliott Gould (2.812), Robert De Niro (2.812), Gene Hackman (2.813), Charlton Heston (2.815)

Kevin Bacon, by the way, is ranked 507 in this list – still placing him as one of the most “centric” Hollywood actors, as there are many other actors with an average shortest path score of 5, 6 and even close to 20 (the data was obtained from “The Oracle Of Bacon” project, at http://oracleofbacon.org/center_list.php).

Actors that have a low average shortest path are therefore “hubs” in the small world network that is derived from Hollywood co-starring. Having a relatively high number of hubs can easily be observed by measuring the fraction of network nodes that have a relatively high degree (e.g. hubs). Networks with a greater than expected number of hubs will have a greater fraction of nodes with high degree, and consequently their degree distribution will be enriched at high degree values. This is known colloquially as a “fat-tailed” distribution.

But what can that tell us about the nature of human communities and interactions? Well, quite a lot actually. Hubs, for example, can serve as centers of information proliferation. Going back to our discussion in social trading, monitoring the behavior of “hubs” can help predict future trading trends of the general population (as trends tend to be generated as a side effect of fast propagation of news or other information).

So, are trading networks small world networks ? Can we find hubs there ? And how many ? These questions were very hard to answer until recently, but thanks to the introduction of eToro’s OpenBook platform, we can now systematically analyze the internal interactions between this community of traders, and have a glimpse at the dynamics that take place there. Following is snapshot taken just a few months after the introduction of the OpenBook’s social network, formed by the “Following” interaction between two traders (chart is shown in a double-log representation). The distribution’s fat tail can clearly be seen, hinting the existence of information hubs!



“Followers” trading network, based on OpenBook data from October 2010

This is a remarkable observation indeed, as it gives us for the first time an evidence that even internet based communities of private traders tend to self-organize themselves in a way that generate hubs (or “trading gurus”). Next – more on what can we do with this understanding.