Clustering coefficient

Clustering coefficient is a property of a node in a network. Roughly speaking it tells how well connected the neighborhood of the node is. If the neighborhood is fully connected, the clustering coefficient is 1 and a value close to 0 means that there are hardly any connections in the neighborhood.

Clustering coefficient of the graph is the average clustering coefficient of all nodes in the graph. Topic map is effectively a graph where each topic is a node and each association is an edge in the graph, thus it makes sense to calculate the clustering coefficient of a topic map.

Formal definition

Consider following graph:

Clustering coefficient of a node is the ratio of number of connections in the neighborhood of a node and the number of connections if the neighborhood was fully connected. Here neighborhood of node A means the nodes that are connected to N but does not include A itself. Note that a fully connected group of n nodes has n*(n-1)/2 connections.

For example, the neighborhood of topic 6 consists of topics 9, 12, 2 and 1. Between these topics there is only one connection, from topic 2 to topic 12. If the four topics were fully connected, that is there would be a connection from each topic to every other topic, there would be 4*3/2=6 connections. Clustering coefficient of topic 6 is therefor 1/6=0.17. Clustering coefficient of topic 1 is 0 because there is no connections at all between topics 0, 6, 11 and 19. Clustering coefficient of topic 3 is 1 because the neighborhood consisting of topics 12, 4 and 13 is fully connected.