This section describes the Common Neighbors algorithm in the Neo4j Labs Graph Algorithms library.
This is documentation for the Graph Algorithms Library, which has been deprecated by the Graph Data Science Library (GDS). 
Common neighbors captures the idea that two strangers who have a friend in common are more likely to be introduced than those who don’t have any friends in common.
The Common Neighbors algorithm was developed by the Neo4j Labs team and is not officially supported. 
This section includes:
It is computed using the following formula:
where N(x)
is the set of nodes adjacent to node x
, and N(y)
is the set of nodes adjacent to node y
.
A value of 0 indicates that two nodes are not close, while higher values indicate nodes are closer.
The library contains a function to calculate closeness between two nodes.
The following will create a sample graph:
MERGE (zhen:Person {name: "Zhen"})
MERGE (praveena:Person {name: "Praveena"})
MERGE (michael:Person {name: "Michael"})
MERGE (arya:Person {name: "Arya"})
MERGE (karin:Person {name: "Karin"})
MERGE (zhen)[:FRIENDS](arya)
MERGE (zhen)[:FRIENDS](praveena)
MERGE (praveena)[:WORKS_WITH](karin)
MERGE (praveena)[:FRIENDS](michael)
MERGE (michael)[:WORKS_WITH](karin)
MERGE (arya)[:FRIENDS](karin)
The following will return the number of common neighbors for Michael and Karin:
MATCH (p1:Person {name: 'Michael'})
MATCH (p2:Person {name: 'Karin'})
RETURN algo.linkprediction.commonNeighbors(p1, p2) AS score
score 

1.0 
We can also compute the score of a pair of nodes based on a specific relationship type.
The following will return the number of common neighbors for Michael and Karin based only on the FRIENDS
relationships:
MATCH (p1:Person {name: 'Michael'})
MATCH (p2:Person {name: 'Karin'})
RETURN algo.linkprediction.commonNeighbors(p1, p2, {relationshipQuery: "FRIENDS"}) AS score
score 

0.0 
The following will run the algorithm and return the result:
RETURN algo.linkprediction.commonNeighbors(node1:Node, node2:Node, {
relationshipQuery: null,
direction: "BOTH"
})
Name  Type  Default  Optional  Description 


Node 
null 
no 
A node 

Node 
null 
no 
Another node 

String 
null 
yes 
The relationship type used to compute similarity between 

String 
BOTH 
yes 
The direction of relationship type used to compute similarity between 