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:
Query.
START a = node(*) MATCH (a)--(b) WITH a, count(distinct b) as n MATCH (a)--()-[r]-()--(a) WHERE a.name! = "startnode" RETURN n, count(distinct r) as r
This returns n and r for the above calculations.
Try this query live. (1) {"name":"startnode"} (2) {} (3) {} (4) {} (5) {} (6) {} (7) {} (1)-[:KNOWS]->(2) {} (1)-[:KNOWS]->(3) {} (1)-[:KNOWS]->(4) {} (1)-[:KNOWS]->(5) {} (2)-[:KNOWS]->(6) {} (2)-[:KNOWS]->(7) {} (3)-[:KNOWS]->(4) {} START a = node(*) MATCH (a)--(b) WITH a, count(distinct b) as n MATCH (a)--()-[r]-()--(a) WHERE a.name! = "startnode" RETURN n, count(distinct r) as r