Tuesday, February 1, 2011

Network Science, Facebook and Economics

In their critique of orthodox method, heterodox economists are faced with the burden of offering alternatives.  By stressing the importance of tradition, consequence and interconnectedness, we agree to the task of accounting for them.  One quest that emerges from this seeks to identify the network of social connections that constitute our environment.  To whom are we connected?  How do we affect the decisions of others?  What goods flow between which connections, and why did they do so at all?

In order to find appropriate methods for addressing these questions I've spent a deal of time lately reading the literature on network analysis. The idea is that if you have a list of nodes - e.g. friends, colleagues, etc. - and a list of their connections, you can begin to see the structure of the network.  For instance, two friends may have a set of common friends, who in turn may have common friends, and so on.  When we think of the degrees of separation, we are referring to the structure of the network.

Out of curiosity I decided to analyze my facebook friends network.  Using netvizz I extracted a graph file that contains my lists of nodes and edges (connections).  Then I imported that into Gephi and ran a few tests on the data.  First, I ran an algorithm that determined the degree of connectedness of each node.  The degree measure is simply the number of connections to other nodes per node.  Next, I sized each node relative to its degree, making larger nodes visible as the most connected.  Then, I ran the force atlas algorithm to distribute the nodes in a manner that makes the network visually meaningful.  Finally, I ran a modularity test.  This detects distinct communities in the network, based upon a neighborhood of mutual connections.  Oh, and I got rid of the names for the sake of anonymity.  Here's what I discovered:

Immediately you'll notice that there about 9 main color groups.  These are the communities that were discovered in the modularity test.  I was pretty amazed at how accurately it identified the communities in my actual friendship network.  For instance, all purple, red, yellow and peach nodes went to my high school.  But, only the purple nodes graduated in 2002, while the red group was in my class of 2000.  Further still, the yellow group singles out the people I knew in high school since middle school.

Overall my facebook network is well connected.  With exception of a few "islands" of friends most of my friends have direct friendships with other friends of mine.  In particular, this network has an average path length of 2.087:  on average people in my network are within 2 degrees of separation.  Each friend is connected to 11 of my other friends on average.

There are four friends in particular that stand out as being much more connected than the group as a whole:  the largest of green, purplish-blue, dark blue and peach.  Their respective degrees are  58, 42, 50, 53.  This isn't terribly surprising given that each of these are my closest friends.  What this graph infers and my experience confirms, is that each of these well connected nodes is my connection to its respective color group.  My large green friend is well connected to my friends from Western, and indeed is responsible for our introduction.  Similarly, my large purple friend is connected to 42 of my high school and family friends.  And the large blue and peach friends are brothers.

The islands of friends share in common no connection to the larger group of high school, family and WWU friends.  They are entirely representative of discontinuous breaks in my past experience.  For instance, the small turquoise pair of friends is drawn from a set of friends I know from my days in the army.  Similarly, that rather lonely set of friends to the right are from Kansas City.  This is not to say that these friends are friendless; they aren't in their respective networks!  They simply don't share too many common friends from previous stages of my life.

This little exercise is exploratory and does not make any substantial claims.  However, some observations may be drawn from these results.  Primarily that distribution matters when we theorize about the structure of the social systems.  In economics, how individuals are connected in social networks plays a part in the flow of resources through the network.

The much more difficult task of identifying and parsing the data from which to develop structural models of the economy remains.