Since attending the talk by Dr. Tufekci on "The New Social Physics", I have been thinking about social capital and how we can quantify it.
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Social Capital, is a term used to describe the intrinsic value of social networks. Robert Putnam attributes social capital to "civic engagement" and as an indicator of "communal health". Pierre Bourdieu describes how social capital explains how people find jobs through their social connections. Similarly, the strength of weak links, describes the importance of social relations in job searches.
In general social capital can be described in terms of bridging capital and bonding capital. Bridging capital is the notion that chance, long range social connections, that we build as part of our social interactions, can help us connect with heterogeneous groups. The idea of "bridges" in social relation is again similar to the notion of connectors in the book "Tipping Point" by Malcolm Gladwell. As Gladwell describes it
"Connectors are people who link us to the world ... people with a special gift for bringing the world together"
So how can we quantify the connectors? According to the Wikipedia entry:
"There is no widely held consensus on how to measure social capital, which is one of its weaknesses."
One simple way to explain such relations is to use the analogy of bridges. These are individuals who link across the different departments in your office, they are the researchers who have worked with people from other fields and universities. We all know such people and run to them to find our link to the "other side of the planet". One measure that might be useful in quantifying bridging capital is "Edge betweenness". It is a measure that indicates the number of all pair shortest paths that flow through an edge. In other words, if the edge is removed, many pairs of nodes need to follow a longer path to communicate with each other. Edge-betweenness is also used in some of the community detection techniques. By iteratively removing edges that are most in-between, we can identify the communities that exist in a social network.
Bridging capital is easier to conceptualize than bonding capital. Bonding capital is defined as
"the value assigned to social networks between homogeneous groups of people"
Another way of thinking about bonding capital is as follows: If you were in an urgent need for $500, which you promised to return the next day -- whom would you turn to? The person most likely to lend you the money is one with whom you share a strong bond. In my opinion, one simple way in which bonding capital can be quantified is by measuring the "strength of ties" or the number of common relations you share with another individual. If we think about business partners, it is quite likely that they share the same set of social relationships. Thus their bonding capital will be quite high. By identifying social relationships, which if removed would cause the least effect in the overall shortest path distance between other nodes, we can identify the edges that have a high bonding capital.
Here is a simple example, from the classic karate club dataset. In this graph there are 34 nodes that represent the members of a karate club. During this study the group split into two with half the members going to the founder of the club, node 34 and the rest to the instructor, node 1. Here we can find interesting examples of bridging and bonding capital. The edge between node 33 and node 34 reflect a high bonding capital.. both these nodes have several friends in common. On the other hand the link from 9 to 1 among others are examples of bridging capital.
I would also like to point out a very interesting piece of research by Dr. Tufekci on social relations in Facebook. According to her study, she found that women use Facebook as a means to establish bonding capital while men are trying to increase bridging capital. This is an excellent study on Facebook from a social science perspective and I would highly recommend reading it.
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