Calculating the Clustering Coefficient of a friend network

In this example, adapted from Niko Gamulins blog post on Neo4j for Social Network Analysis, the graph in question is showing the 2-hop relationships of a sample person as nodes with KNOWS relationships. The clustering coefficient of a selected node is defined as the probability that two randomly selected neighbors are connected to each other. With the number of neighbors as n and the number of mutual connections between the neighbors r the calculation is the number of possible connections between two neighbors is n!/(2!(n-2)!) = 4!/(2!(4-2)!) = 24/4 = 6, where n is the number of neighbors n = 4 and the actual number r of connections is 1. Therefore, the clustering coefficient of node 1 is 1/6. n and r are quite simple to retrieve via the following query:

MATCH (a {name: "startnode"})--(b)
WITH a, count(distinct b) AS n
MATCH (a)--()-[r]-()--(a)
RETURN n, count(distinct r) AS r

This returns n and r for the above calculations.