Preferential Attachment

This feature is not available in Aura Graph Analytics.

Preferential Attachment is a measure used to compute the closeness of nodes, based on their shared neighbors.

History and explanation

Preferential attachment means that the more connected a node is, the more likely it is to receive new links. This algorithm was popularised by Albert-László Barabási and Réka Albert through their work on scale-free networks. 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 that nodes are closer.

The library contains a function to calculate closeness between two nodes.

Syntax

The following will run the algorithm and return the result:

RETURN gds.linkprediction.preferentialAttachment(node1:Node, node2:Node, {
    relationshipQuery:String,
    direction:String
})

Table 1. Parameters
Name	Type	Default	Optional	Description
`node1`	Node	null	no	A node
`node2`	Node	null	no	Another node
`relationshipQuery`	String	null	yes	The relationship type used to compute similarity between `node1` and `node2`
`direction`	String	BOTH	yes	The relationship direction used to compute similarity between `node1` and `node2`. Possible values are `OUTGOING`, `INCOMING` and `BOTH`.

Preferential Attachment algorithm sample

The following will create a sample graph:

CREATE
 (zhen:Person {name: 'Zhen'}),
 (praveena:Person {name: 'Praveena'}),
 (michael:Person {name: 'Michael'}),
 (arya:Person {name: 'Arya'}),
 (karin:Person {name: 'Karin'}),

 (zhen)-[:FRIENDS]->(arya),
 (zhen)-[:FRIENDS]->(praveena),
 (praveena)-[:WORKS_WITH]->(karin),
 (praveena)-[:FRIENDS]->(michael),
 (michael)-[:WORKS_WITH]->(karin),
 (arya)-[:FRIENDS]->(karin)

The following will return the Preferential Attachment score for Michael and Karin:

 MATCH (p1:Person {name: 'Michael'})
 MATCH (p2:Person {name: 'Karin'})
 RETURN gds.linkprediction.preferentialAttachment(p1, p2) AS score

Table 2. Results
`score`
6.0

We can also compute the score of a pair of nodes based on a specific relationship type.

The following will return the Preferential Attachment score for Michael and Karin based only on the FRIENDS relationship:

 MATCH (p1:Person {name: 'Michael'})
 MATCH (p2:Person {name: 'Karin'})
 RETURN gds.linkprediction.preferentialAttachment(p1, p2, {relationshipQuery: "FRIENDS"}) AS score

Table 3. Results
`score`
1.0