Quantifying clustering in a network

There are various quantities associated with networks that measure the characteristics of the network. For example, the clustering coefficient of a node measures the interconnectivity between the nodes nearby (here, nearby means connected by an edge). In effect, it measures how close the neighboring nodes are to forming a complete network or clique.

The clustering coefficient of a node measures the proportion of the adjacent nodes that are connected by an edge; that is, two adjacent nodes form a triangle with the given node. We count the number of triangles and divide this by the total number of possible triangles that could be formed, given the degree of the node. Numerically, the clustering coefficient at a node, u, in a simple unweighted network is given by the following equation:

Here, T_u is the number of triangles at u and the denominator is the total possible number of triangles at u. If the...