This section describes the Adamic Adar algorithm in the Neo4j Labs Graph Algorithms library.
Adamic Adar is a measure used to compute the closeness of nodes based on their shared neighbors.
The Adamic Adar algorithm was developed by the Neo4j Labs team and is not officially supported. 
This section includes:
The Adamic Adar algorithm was introduced in 2003 by Lada Adamic and Eytan Adar to predict links in a social network. It is computed using the following formula:
where N(u)
is the set of nodes adjacent to u
.
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 Adamic Adar score for Michael and Karin:
MATCH (p1:Person {name: 'Michael'})
MATCH (p2:Person {name: 'Karin'})
RETURN algo.linkprediction.adamicAdar(p1, p2) AS score
score 

1.4426950408889634 
We can also compute the score of a pair of nodes based on a specific relationship type.
The following will return the Adamic Adar score for Michael and Karin based only on the FRIENDS
relationships:
MATCH (p1:Person {name: 'Michael'})
MATCH (p2:Person {name: 'Karin'})
RETURN algo.linkprediction.adamicAdar(p1, p2, {relationshipQuery: "FRIENDS"}) AS score
score 

0.0 
The following will run the algorithm and return the result:
RETURN algo.linkprediction.adamicAdar(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 