# Random Walk

## Glossary

Directed

Directed trait. The algorithm is well-defined on a directed graph.

Directed

Directed trait. The algorithm ignores the direction of the graph.

Directed

Directed trait. The algorithm does not run on a directed graph.

Undirected

Undirected trait. The algorithm is well-defined on an undirected graph.

Undirected

Undirected trait. The algorithm ignores the undirectedness of the graph.

Heterogeneous nodes

Heterogeneous nodes fully supported. The algorithm has the ability to distinguish between nodes of different types.

Heterogeneous nodes

Heterogeneous nodes allowed. The algorithm treats all selected nodes similarly regardless of their label.

Heterogeneous relationships

Heterogeneous relationships fully supported. The algorithm has the ability to distinguish between relationships of different types.

Heterogeneous relationships

Heterogeneous relationships allowed. The algorithm treats all selected relationships similarly regardless of their type.

Weighted relationships

Weighted trait. The algorithm supports a relationship property to be used as weight, specified via the relationshipWeightProperty configuration parameter.

Weighted relationships

Weighted trait. The algorithm treats each relationship as equally important, discarding the value of any relationship weight.

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.

## Syntax

RandomWalk syntax per mode
Run RandomWalk in stream mode on a named graph.
``````CALL gds.randomWalk.stream(
graphName: String,
configuration: Map
)
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. Nodes with any of the given labels will be included.

relationshipTypes

List of String

`['*']`

yes

Filter the named graph using the given relationship types. Relationships with any of the given types will be included.

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.

logProgress

Boolean

`true`

yes

If disabled the progress percentage will not be logged.

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.

Run RandomWalk in stats mode on a named graph.
``````CALL gds.randomWalk.stats(
graphName: String,
configuration: Map
)
YIELD
preProcessingMillis: Integer,
computeMillis: Integer,
configuration: Map``````
Table 4. 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 5. Configuration
Name Type Default Optional Description

nodeLabels

List of String

`['*']`

yes

Filter the named graph using the given node labels. Nodes with any of the given labels will be included.

relationshipTypes

List of String

`['*']`

yes

Filter the named graph using the given relationship types. Relationships with any of the given types will be included.

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.

logProgress

Boolean

`true`

yes

If disabled the progress percentage will not be logged.

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 6. Results
Name Type Description

`preProcessingMillis`

Integer

Milliseconds for preprocessing the data.

`computeMillis`

Integer

Milliseconds for running the algorithm.

`configuration`

Map

The configuration used for running the algorithm.

## Examples

 All the examples below should be run in an empty database. The examples use native projections as the norm, although Cypher projections can be used as well.

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' } }
);``````

### Without specified source nodes

Run the RandomWalk algorithm on `myGraph`
``````CALL gds.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 7. Results
nodeIds pages

[0, 5, 0]

["Home", "Site B", "Home"]

[1, 0, 4]

[2, 0, 3]

[3, 7, 3]

[4, 3, 0]

[5, 0, 2]

["Site B", "Home", "Product"]

[6, 0, 4]

["Site C", "Home", "Site A"]

[7, 0, 2]

["Site D", "Home", "Product"]

### With specified source nodes

Run the RandomWalk algorithm on `myGraph` with specified sourceNodes
``````MATCH (page:Page)
WITH COLLECT(page) as sourceNodes
CALL gds.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 8. Results
nodeIds pages

[0, 5, 0]

["Home", "Site B", "Home"]

[1, 0, 4]

### Stats

Run the RandomWalk stats on `myGraph`
``````CALL gds.randomWalk.stats(
'myGraph',
{
walkLength: 3,
walksPerNode: 1,
randomSeed: 42,
concurrency: 1
}
)``````
Table 9. Results
preProcessingMillis computeMillis configuration

0

1

{randomSeed=42, walkLength=3, jobId=b77f3147-6683-4249-8633-4db7da03f24d, sourceNodes=[], walksPerNode=1, inOutFactor=1.0, nodeLabels=[], sudo=false, relationshipTypes=[], walkBufferSize=1000, returnFactor=1.0, concurrency=1}