Figure 6.10. Graph
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
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.
Result
| n | r |
|---|---|
| 1 row | |
|
|
Try this query live create (_0 {`name`:"startnode"}) create (_1) create (_2) create (_3) create (_4) create (_5) create (_6) create (_0)-[:`KNOWS`]->(_4) create (_0)-[:`KNOWS`]->(_3) create (_0)-[:`KNOWS`]->(_2) create (_0)-[:`KNOWS`]->(_1) create (_1)-[:`KNOWS`]->(_6) create (_1)-[:`KNOWS`]->(_5) create (_2)-[:`KNOWS`]->(_3) ; MATCH (a {name: "startnode"})--(b) WITH a, count(distinct b) as n MATCH (a)--()-[r]-()--(a) RETURN n, count(distinct r) as r