# Random Walk

Random Walk is an algorithm that provides random paths in a graph.

A random walk simulates a traversal of the graph in which the traversed relationships are chosen at random. In a classic random walk, each relationship has the same, possibly weighted, probability of being picked. This probability is not influenced by the previously visited nodes. The random walk implementation of the Neo4j Graph Data Science library supports the concept of second order random walks. This method tries to model the transition probability based on the currently visited node `v`, the node `t` visited before the current one, and the node `x` which is the target of a candidate relationship. Random walks are thus influenced by two parameters: the `returnFactor` and the `inOutFactor`:

• The `returnFactor` is used if `t` equals `x`, i.e., the random walk returns to the previously visited node.

• The `inOutFactor` is used if the distance from `t` to `x` is equal to 2, i.e., the walk traverses further away from the node `t`

The probabilities for traversing a relationship during a random walk can be further influenced by specifying a `relationshipWeightProperty`. A relationship property value greater than 1 will increase the likelihood of a relationship being traversed, a property value between 0 and 1 will decrease that probability.

 To obtain a random walk where the transition probability is independent of the previously visited nodes both the `returnFactor` and the `inOutFactor` can be set to 1.0.
 Running this algorithm requires sufficient memory availability. Before running this algorithm, we recommend that you read Memory Estimation.

## 1. Syntax

RandomWalk syntax per mode
Run RandomWalk in stream mode on a named graph.
``````CALL gds.beta.randomWalk.stream(
graphName: String,
configuration: Map
) YIELD
YIELD
nodeIds: List of Integer,
path: Path``````
Table 1. Parameters
Name Type Default Optional Description

graphName

String

`n/a`

no

The name of a graph stored in the catalog.

configuration

Map

`{}`

yes

Configuration for algorithm-specifics and/or graph filtering.

Table 2. Configuration
Name Type Default Optional Description

nodeLabels

List of String

`['*']`

yes

Filter the named graph using the given node labels.

relationshipTypes

List of String

`['*']`

yes

Filter the named graph using the given relationship types.

concurrency

Integer

`4`

yes

The number of concurrent threads used for running the algorithm.

jobId

String

`Generated internally`

yes

An ID that can be provided to more easily track the algorithm’s progress.

sourceNodes

List of Integer

`List of all nodes`

yes

The list of nodes from which to do a random walk.

walkLength

Integer

`80`

yes

The number of steps in a single random walk.

walksPerNode

Integer

`10`

yes

The number of random walks generated for each node.

inOutFactor

Float

`1.0`

yes

Tendency of the random walk to stay close to the start node or fan out in the graph. Higher value means stay local.

returnFactor

Float

`1.0`

yes

Tendency of the random walk to return to the last visited node. A value below 1.0 means a higher tendency.

relationshipWeightProperty

String

`null`

yes

Name of the relationship property to use as weights to influence the probabilities of the random walks. The weights need to be >= 0. If unspecified, the algorithm runs unweighted.

randomSeed

Integer

`random`

yes

Seed value for the random number generator used to generate the random walks.

walkBufferSize

Integer

`1000`

yes

The number of random walks to complete before starting training.

Table 3. Results
Name Type Description

`nodeIds`

List of Integer

The nodes of the random walk.

`path`

Path

A `Path` object of the random walk.

## 2. Examples

Consider the graph created by the following Cypher statement:

``````CREATE (home:Page {name: 'Home'}),
(product:Page {name: 'Product'}),
(a:Page {name: 'Site A'}),
(b:Page {name: 'Site B'}),
(c:Page {name: 'Site C'}),
(d:Page {name: 'Site D'}),

``````CALL gds.graph.project(
'myGraph',
'*',
{ LINKS: { orientation: 'UNDIRECTED' } }
);``````

### 2.1. Without specified source nodes

Run the RandomWalk algorithm on `myGraph`
``````CALL gds.beta.randomWalk.stream(
'myGraph',
{
walkLength: 3,
walksPerNode: 1,
randomSeed: 42,
concurrency: 1
}
)
YIELD nodeIds, path
RETURN nodeIds, [node IN nodes(path) | node.name ] AS pages``````
Table 4. Results
nodeIds pages

[0, 5, 3]

[1, 0, 6]

[2, 0, 5]

[Product, Home, Site B]

[3, 6, 3]

[4, 3, 4]

[5, 3, 5]

[6, 3, 7]

[7, 3, 0]

### 2.2. With specified source nodes

Run the RandomWalk algorithm on `myGraph` with specified sourceNodes
``````MATCH (page:Page)
WITH COLLECT(page) as sourceNodes
CALL gds.beta.randomWalk.stream(
'myGraph',
{
sourceNodes: sourceNodes,
walkLength: 3,
walksPerNode: 1,
randomSeed: 42,
concurrency: 1
}
)
YIELD nodeIds, path
RETURN nodeIds, [node IN nodes(path) | node.name ] AS pages``````
Table 5. Results
nodeIds pages

[0, 5, 3]