Node2Vec

This section describes the Node2Vec node embedding algorithm in the Neo4j Graph Data Science library.

Node2Vec is a node embedding algorithm that computes a vector representation of a node based on random walks in the graph. The neighborhood is sampled through random walks. Using a number of random neighborhood samples, the algorithm trains a single hidden layer neural network. The neural network is trained to predict the likelihood that a node will occur in a walk based on the occurrence of another node.

For more information on this algorithm, see:

1. Random Walks

A main concept of the Node2Vec algorithm are the second order random walks. 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 concept of second order random walks, however, 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. Node2Vec 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.

For every node in the graph Node2Vec generates a series of random walks with the particular node as start node. The number of random walks per node can be influenced by the walkPerNode configuration parameters, the walk length is controlled by the walkLength parameter.

2. Syntax

Node2Vec syntax per mode

Run Node2Vec in stream mode on a named graph.

CALL gds.beta.node2vec.stream(
  graphName: String,
  configuration: Map
) YIELD
  nodeId: Integer,
  embedding: List of Float

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. General configuration for algorithm execution on a named graph.
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.

Table 3. Algorithm specific configuration
Name	Type	Default	Optional	Description
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.
windowSize	Integer	`10`	yes	Size of the context window when training the neural network.
negativeSamplingRate	Integer	`5`	yes	Number of negative samples to produce for each positive sample.
positiveSamplingFactor	Float	`0.001`	yes	Factor for influencing the distribution for positive samples. A higher value increases the probability that frequent nodes are down-sampled.
negativeSamplingExponent	Float	`0.75`	yes	Exponent applied to the node frequency to obtain the negative sampling distribution. A value of 1.0 samples proportionally to the frequency. A value of 0.0 samples each node equally.
embeddingDimension	Integer	`128`	yes	Size of the computed node embeddings.
iterations	Integer	`1`	yes	Number of training iterations.
initialLearningRate	Float	`0.01`	yes	Learning rate used initially for training the neural network. The learning rate decreases after each training iteration.
minLearningRate	Float	`0.0001`	yes	Lower bound for learning rate as it is decreased during training.
randomSeed	Integer	`random`	yes	Seed value used to generate the random walks, which are used as the training set of the neural network. Note, that the generated embeddings are still nondeterministic.
walkBufferSize	Integer	`1000`	yes	The number of random walks to complete before starting training.

Table 4. Results
Name	Type	Description
`nodeId`	Integer	The Neo4j node ID.
`embedding`	List of Float	The computed node embedding.

Run Node2Vec in mutate mode on a graph stored in the catalog.

CALL gds.beta.node2vec.mutate(
  graphName: String,
  configuration: Map
)
YIELD
  preProcessingMillis: Integer,
  computeMillis: Integer,
  postProcessingMillis: Integer,
  mutateMillis: Integer,
  nodeCount: Integer,
  nodePropertiesWritten: Integer,
  configuration: Map

Table 5. 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 6. General configuration for algorithm execution on a named graph.
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.
mutateProperty	String	`n/a`	no	The node property in the GDS graph to which the embedding is written.

Table 7. Algorithm specific configuration
Name	Type	Default	Optional	Description
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.
windowSize	Integer	`10`	yes	Size of the context window when training the neural network.
negativeSamplingRate	Integer	`5`	yes	Number of negative samples to produce for each positive sample.
positiveSamplingFactor	Float	`0.001`	yes	Factor for influencing the distribution for positive samples. A higher value increases the probability that frequent nodes are down-sampled.
negativeSamplingExponent	Float	`0.75`	yes	Exponent applied to the node frequency to obtain the negative sampling distribution. A value of 1.0 samples proportionally to the frequency. A value of 0.0 samples each node equally.
embeddingDimension	Integer	`128`	yes	Size of the computed node embeddings.
iterations	Integer	`1`	yes	Number of training iterations.
initialLearningRate	Float	`0.01`	yes	Learning rate used initially for training the neural network. The learning rate decreases after each training iteration.
minLearningRate	Float	`0.0001`	yes	Lower bound for learning rate as it is decreased during training.
randomSeed	Integer	`random`	yes	Seed value used to generate the random walks, which are used as the training set of the neural network. Note, that the generated embeddings are still nondeterministic.
walkBufferSize	Integer	`1000`	yes	The number of random walks to complete before starting training.

Table 8. Results
Name	Type	Description
nodeCount	Integer	The number of nodes processed.
nodePropertiesWritten	Integer	The number of node properties written.
preProcessingMillis	Integer	Milliseconds for preprocessing the data.
computeMillis	Integer	Milliseconds for running the algorithm.
mutateMillis	Integer	Milliseconds for adding properties to the projected graph.
postProcessingMillis	Integer	Milliseconds for post-processing of the results.
configuration	Map	The configuration used for running the algorithm.

Run Node2Vec in write mode on a graph stored in the catalog.

CALL gds.beta.node2vec.write(
  graphName: String,
  configuration: Map
)
YIELD
  preProcessingMillis: Integer,
  computeMillis: Integer,
  writeMillis: Integer,
  nodeCount: Integer,
  nodePropertiesWritten: Integer,
  configuration: Map

Table 9. 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 10. General configuration for algorithm execution on a named graph.
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. Also provides the default value for 'writeConcurrency'.
writeConcurrency	Integer	`value of 'concurrency'`	yes	The number of concurrent threads used for writing the result to Neo4j.
writeProperty	String	`n/a`	no	The node property in the Neo4j database to which the embedding is written.

Table 11. Algorithm specific configuration
Name	Type	Default	Optional	Description
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.
windowSize	Integer	`10`	yes	Size of the context window when training the neural network.
negativeSamplingRate	Integer	`5`	yes	Number of negative samples to produce for each positive sample.
positiveSamplingFactor	Float	`0.001`	yes	Factor for influencing the distribution for positive samples. A higher value increases the probability that frequent nodes are down-sampled.
negativeSamplingExponent	Float	`0.75`	yes	Exponent applied to the node frequency to obtain the negative sampling distribution. A value of 1.0 samples proportionally to the frequency. A value of 0.0 samples each node equally.
embeddingDimension	Integer	`128`	yes	Size of the computed node embeddings.
iterations	Integer	`1`	yes	Number of training iterations.
initialLearningRate	Float	`0.01`	yes	Learning rate used initially for training the neural network. The learning rate decreases after each training iteration.
minLearningRate	Float	`0.0001`	yes	Lower bound for learning rate as it is decreased during training.
randomSeed	Integer	`random`	yes	Seed value used to generate the random walks, which are used as the training set of the neural network. Note, that the generated embeddings are still nondeterministic.
walkBufferSize	Integer	`1000`	yes	The number of random walks to complete before starting training.

Table 12. Results
Name	Type	Description
nodeCount	Integer	The number of nodes processed.
nodePropertiesWritten	Integer	The number of node properties written.
preProcessingMillis	Integer	Milliseconds for preprocessing the data.
computeMillis	Integer	Milliseconds for running the algorithm.
writeMillis	Integer	Milliseconds for writing result data back to Neo4j.
configuration	Map	The configuration used for running the algorithm.

3. Examples

Consider the graph created by the following Cypher statement:

CREATE (alice:Person {name: 'Alice'})
CREATE (bob:Person {name: 'Bob'})
CREATE (carol:Person {name: 'Carol'})
CREATE (dave:Person {name: 'Dave'})
CREATE (eve:Person {name: 'Eve'})
CREATE (guitar:Instrument {name: 'Guitar'})
CREATE (synth:Instrument {name: 'Synthesizer'})
CREATE (bongos:Instrument {name: 'Bongos'})
CREATE (trumpet:Instrument {name: 'Trumpet'})

CREATE (alice)-[:LIKES]->(guitar)
CREATE (alice)-[:LIKES]->(synth)
CREATE (alice)-[:LIKES]->(bongos)
CREATE (bob)-[:LIKES]->(guitar)
CREATE (bob)-[:LIKES]->(synth)
CREATE (carol)-[:LIKES]->(bongos)
CREATE (dave)-[:LIKES]->(guitar)
CREATE (dave)-[:LIKES]->(synth)
CREATE (dave)-[:LIKES]->(bongos);

CALL gds.graph.project('myGraph', ['Person', 'Instrument'], 'LIKES');

Run the Node2Vec algorithm on myGraph

CALL gds.beta.node2vec.stream('myGraph', {embeddingDimension: 2})
YIELD nodeId, embedding
RETURN nodeId, embedding

Table 13. Results
nodeId	embedding
0	[-0.14295829832553864, 0.08884537220001221]
1	[0.016700705513358116, 0.2253911793231964]
2	[-0.06589698046445847, 0.042405471205711365]
3	[0.05862073227763176, 0.1193704605102539]
4	[0.10888434946537018, -0.18204474449157715]
5	[0.16728264093399048, 0.14098615944385529]
6	[-0.007779224775731564, 0.02114257402718067]
7	[-0.213893860578537, 0.06195802614092827]
8	[0.2479933649301529, -0.137322798371315]

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