I was reading papers written by the eminent sociologists, Ronald Burt (of the University of Chicago Booth School of Business) and Peter Marsden (Harvard University) on social networks and social capital and thought I’d share my thoughts on their application in today’s connected social milieu. However, I realized that before I did that, it might help to get a basic understanding of commonly used network properties. Hence, this post is meant to provide a refresher/primer on certain core network-related concepts.
As everyone knows, networks are composed of nodes (entities) and edges (relationships between the nodes) as shown in the figure above. A network with edges that do not have arrows or directionality (like the one above) is called an un-directed network. Networks with directed edges are called (surprise! surprise!), directed networks.
So how do we study the relative importance of people in social networks like these? Are more number of connections always better? Or are the quality of connections more important? Does it matter who you know? Does it matter both about who you know and where that person exists? To answer questions like these, researchers have come up with a number of measures that describe the relative position of an individual in the network. I am going to describe 5 of the most commonly used measures.
The degree of a node is simply the number of connections that node has. In the figure on the left (the undirected network), node d has a degree of 7. For directed networks though, degree has been split into in-degree (number of incoming connections and out-degree (the number of outgoing connections). For the node d in the network on the right. the in-degree is 2 and the out-degree, 5.
Clustering Coefficient (CC)
The clustering coefficient is a measure of how connected or tightly bound a person is in his or her neighbourhood (locality). It is calculated by taking all the connections in a node’s neighbourhood and dividing that by the number of all possible connections. In an organizational context, one would expect junior members in a team or function to have a high clustering coefficient since they would be linked more to other members in their team than to those outside the team.
Betweenness Centrality (BC)
Betweeness is a measure of the importance of a node for “communication” in a network. People with high betweeness centrality measures act as bridges between different parts of the organization. For example, the red node is an important hub in the blue subnetwork. However, the orange and yellow nodes will have a higher BC because they are the ones that connect the two different subnetworks. This is an extremely important measure in the context of the work done by Professor Burt.
I like to think of eigen-centrality as a measure of network leadership. People with high eigen-centrality are those who are connected to other network leaders. Think of it as highly-connected people, connecting to other highly-connected people. In the diagram above, the red circle and diamond, would have high eigen-centrality values since they are each highly connected individuals.
That’s about it basically. With this understanding, I’d like to look at some of the interesting insights from Prof. Burt’s papers in future posts.