This section describes the Total Neighbors algorithm in the Neo4j Labs Graph Algorithms library.
Total Neighbors computes the closeness of nodes, based on the number of unique neighbors that they have. It is based on the idea that the more connected a node is, the more likely it is to receive new links.
The Total Neighbors algorithm was developed by the Neo4j Labs team and is not officially supported. 
This section includes:
Total Neighbors is computed using the following formula:
where N(x)
is the set of nodes adjacent to x
, and N(y)
is the set of nodes adjacent to 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 the 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 Total Neighbors score for Michael and Karin:
MATCH (p1:Person {name: 'Michael'})
MATCH (p2:Person {name: 'Karin'})
RETURN algo.linkprediction.totalNeighbors(p1, p2) AS score
score 

4.0 
We can also compute the score of a pair of nodes, based on a specific relationship type.
The following will return the Total Neighbors score for Michael and Karin based only on the FRIENDS
relationship:
MATCH (p1:Person {name: 'Michael'})
MATCH (p2:Person {name: 'Karin'})
RETURN algo.linkprediction.totalNeighbors(p1, p2, {relationshipQuery: "FRIENDS"}) AS score
score 

2.0 
The following will run the algorithm and return the result:
RETURN algo.linkprediction.totalNeighbors(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 