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 ift
equalsx
, i.e., the random walk returns to the previously visited node. 
The
inOutFactor
is used if the distance fromt
tox
is equal to 2, i.e., the walk traverses further away from the nodet
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
CALL gds.randomWalk.stream(
graphName: String,
configuration: Map
)
YIELD
nodeIds: List of Integer,
path: Path
Name  Type  Default  Optional  Description 

graphName 
String 

no 
The name of a graph stored in the catalog. 
configuration 
Map 

yes 
Configuration for algorithmspecifics and/or graph filtering. 
Name  Type  Default  Optional  Description 

List of String 

yes 
Filter the named graph using the given node labels. 

List of String 

yes 
Filter the named graph using the given relationship types. 

Integer 

yes 
The number of concurrent threads used for running the algorithm. 

String 

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

sourceNodes 
List of Integer 

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

yes 
The number of steps in a single random walk. 
walksPerNode 
Integer 

yes 
The number of random walks generated for each node. 
inOutFactor 
Float 

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 

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

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 

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

yes 
The number of random walks to complete before starting training. 
Name  Type  Description 


List of Integer 
The nodes of the random walk. 

Path 
A 
CALL gds.randomWalk.stats(
graphName: String,
configuration: Map
)
YIELD
preProcessingMillis: Integer,
computeMillis: Integer,
configuration: Map
Name  Type  Default  Optional  Description 

graphName 
String 

no 
The name of a graph stored in the catalog. 
configuration 
Map 

yes 
Configuration for algorithmspecifics and/or graph filtering. 
Name  Type  Default  Optional  Description 

List of String 

yes 
Filter the named graph using the given node labels. 

List of String 

yes 
Filter the named graph using the given relationship types. 

Integer 

yes 
The number of concurrent threads used for running the algorithm. 

String 

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

sourceNodes 
List of Integer 

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

yes 
The number of steps in a single random walk. 
walksPerNode 
Integer 

yes 
The number of random walks generated for each node. 
inOutFactor 
Float 

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 

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

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 

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

yes 
The number of random walks to complete before starting training. 
Name  Type  Description 


Integer 
Milliseconds for preprocessing the data. 

Integer 
Milliseconds for running the algorithm. 

Map 
The configuration used for running the algorithm. 
2. Examples
Consider the graph created by the following Cypher statement:
CREATE (home:Page {name: 'Home'}),
(about:Page {name: 'About'}),
(product:Page {name: 'Product'}),
(links:Page {name: 'Links'}),
(a:Page {name: 'Site A'}),
(b:Page {name: 'Site B'}),
(c:Page {name: 'Site C'}),
(d:Page {name: 'Site D'}),
(home)[:LINKS]>(about),
(about)[:LINKS]>(home),
(product)[:LINKS]>(home),
(home)[:LINKS]>(product),
(links)[:LINKS]>(home),
(home)[:LINKS]>(links),
(links)[:LINKS]>(a),
(a)[:LINKS]>(home),
(links)[:LINKS]>(b),
(b)[:LINKS]>(home),
(links)[:LINKS]>(c),
(c)[:LINKS]>(home),
(links)[:LINKS]>(d),
(d)[:LINKS]>(home)
CALL gds.graph.project(
'myGraph',
'*',
{ LINKS: { orientation: 'UNDIRECTED' } }
);
2.1. Without specified source nodes
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
nodeIds  pages 

[0, 5, 0] 
[Home, Site B, Home] 
[1, 0, 4] 
[About, Home, Site A] 
[2, 0, 3] 
[Product, Home, Links] 
[3, 7, 3] 
[Links, Site D, Links] 
[4, 3, 0] 
[Site A, Links, Home] 
[5, 0, 2] 
[Site B, Home, Product] 
[6, 0, 4] 
[Site C, Home, Site A] 
[7, 0, 2] 
[Site D, Home, Product] 
2.2. With specified source nodes
myGraph
with specified sourceNodesMATCH (page:Page)
WHERE page.name IN ['Home', 'About']
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
nodeIds  pages 

[0, 5, 0] 
[Home, Site B, Home] 
[1, 0, 4] 
[About, Home, Site A] 
2.3. Stats
myGraph
CALL gds.randomWalk.stats(
'myGraph',
{
walkLength: 3,
walksPerNode: 1,
randomSeed: 42,
concurrency: 1
}
)
preProcessingMillis  computeMillis  configuration 

0 
1 
{randomSeed=42, walkLength=3, jobId=b77f31476683424986334db7da03f24d, sourceNodes=[], walksPerNode=1, inOutFactor=1.0, nodeLabels=[], sudo=false, relationshipTypes=[], walkBufferSize=1000, returnFactor=1.0, concurrency=1} 
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