1. Local Clustering Coefficient
Clustering coefficient for a specific vertex, C(i)
Mean probability that a pair of i’s friends are friends of one another
Average local clustering coefficient over all vertices
This definition (by Watts and Strogatz) came before Global Clustering Coefficient definition
Slide courtesy of Dr. Tim Chung

2. Global Clustering Coefficient
Fraction of the paths of length two in the graph that are closed
A “closed triad” is a closed path of length three through vertices i, j, and k
Calculation
Count all paths of length two, count how many of these are closed, and take their ratio i j k
closed triad
Probability that two vertices with a common adjacent vertex are themselves adjacent
Slide courtesy of Dr. Tim Chung