### 9.6.3. The Preferential Attachment algorithm

This section describes the Preferential Attachment algorithm in the Neo4j Labs Graph Algorithms library.

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

 The Preferential Attachment algorithm was developed by the Neo4j Labs team and is not officially supported.

This section includes:

#### 9.6.3.1. 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.

#### 9.6.3.2. Preferential Attachment algorithm sample

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 Preferential Attachment score for Michael and Karin:

``````MATCH (p1:Person {name: 'Michael'})
MATCH (p2:Person {name: 'Karin'})

Table 9.163. 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 algo.linkprediction.preferentialAttachment(p1, p2, {relationshipQuery: "FRIENDS"}) AS score``````

Table 9.164. Results
`score`

1.0

#### 9.6.3.3. Syntax

The following will run the algorithm and return the result:

``````RETURN algo.linkprediction.preferentialAttachment(node1:Node, node2:Node, {
relationshipQuery: null,
direction: "BOTH"
})``````

Table 9.165. 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 direction of relationship type used to compute similarity between `node1` and `node2`