Label Propagation

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.

Introduction

The Label Propagation algorithm (LPA) is a fast algorithm for finding communities in a graph. It detects these communities using network structure alone as its guide, and doesn’t require a pre-defined objective function or prior information about the communities.

LPA works by propagating labels throughout the network and forming communities based on this process of label propagation.

The intuition behind the algorithm is that a single label can quickly become dominant in a densely connected group of nodes, but will have trouble crossing a sparsely connected region. Labels will get trapped inside a densely connected group of nodes, and those nodes that end up with the same label when the algorithms finish can be considered part of the same community.

The algorithm works as follows:

Every node is initialized with a unique community label (an identifier).
These labels propagate through the network.
At every iteration of propagation, each node updates its label to the one that the maximum numbers of its neighbours belongs to. Ties are broken arbitrarily but deterministically.
LPA reaches convergence when each node has the majority label of its neighbours.
LPA stops if either convergence, or the user-defined maximum number of iterations is achieved.

As labels propagate, densely connected groups of nodes quickly reach a consensus on a unique label. At the end of the propagation only a few labels will remain - most will have disappeared. Nodes that have the same community label at convergence are said to belong to the same community.

One interesting feature of LPA is that nodes can be assigned preliminary labels to narrow down the range of solutions generated. This means that it can be used as semi-supervised way of finding communities where we hand-pick some initial communities.

For more information on this algorithm, see:

Running this algorithm requires sufficient memory availability. Before running this algorithm, we recommend that you read Memory Estimation.

Syntax

This section covers the syntax used to execute the Label Propagation algorithm in each of its execution modes. We are describing the named graph variant of the syntax. To learn more about general syntax variants, see Syntax overview.

Label Propagation syntax per mode

Run Label Propagation in stream mode on a named graph.

CALL gds.labelPropagation.stream(
  graphName: String,
  configuration: Map
)
YIELD
    nodeId: Integer,
    communityId: Integer

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.
maxIterations	Integer	`10`	yes	The maximum number of iterations to run.
nodeWeightProperty	String	`null`	yes	The name of a node property that contains node weights.
relationshipWeightProperty	String	`null`	yes	Name of the relationship property to use as weights. If unspecified, the algorithm runs unweighted.
seedProperty	String	`n/a`	yes	The name of a node property that defines an initial numeric label.
consecutiveIds	Boolean	`false`	yes	Flag to decide whether component identifiers are mapped into a consecutive id space (requires additional memory).
minCommunitySize	Integer	`0`	yes	Only nodes inside communities larger or equal the given value are returned.

Table 3. Results
Name	Type	Description
nodeId	Integer	Node ID.
communityId	Integer	Community ID.

Run Label Propagation in stats mode on a named graph.

CALL gds.labelPropagation.stats(
  graphName: String,
  configuration: Map
)
YIELD
  preProcessingMillis: Integer,
  computeMillis: Integer,
  postProcessingMillis: Integer,
  communityCount: Integer,
  ranIterations: Integer,
  didConverge: Boolean,
  communityDistribution: Map,
  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.
maxIterations	Integer	`10`	yes	The maximum number of iterations to run.
nodeWeightProperty	String	`null`	yes	The name of a node property that contains node weights.
relationshipWeightProperty	String	`null`	yes	Name of the relationship property to use as weights. If unspecified, the algorithm runs unweighted.
seedProperty	String	`n/a`	yes	The name of a node property that defines an initial numeric label.
consecutiveIds	Boolean	`false`	yes	Flag to decide whether component identifiers are mapped into a consecutive id space (requires additional memory).

Table 6. Results
Name	Type	Description
preProcessingMillis	Integer	Milliseconds for preprocessing the data.
computeMillis	Integer	Milliseconds for running the algorithm.
postProcessingMillis	Integer	Milliseconds for computing percentiles and community count.
communityCount	Integer	The number of communities found.
ranIterations	Integer	The number of iterations that were executed.
didConverge	Boolean	True if the algorithm did converge to a stable labelling within the provided number of maximum iterations.
communityDistribution	Map	Map containing min, max, mean as well as p1, p5, p10, p25, p50, p75, p90, p95, p99 and p999 percentile values of community size.
configuration	Map	The configuration used for running the algorithm.

Run Label Propagation in mutate mode on a named graph.

CALL gds.labelPropagation.mutate(
  graphName: String,
  configuration: Map
)
YIELD
  preProcessingMillis: Integer,
  computeMillis: Integer,
  mutateMillis: Integer,
  postProcessingMillis: Integer,
  nodePropertiesWritten: Integer,
  communityCount: Integer,
  ranIterations: Integer,
  didConverge: Boolean,
  communityDistribution: Map,
  configuration: Map

Table 7. 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 8. Configuration
Name	Type	Default	Optional	Description
mutateProperty	String	`n/a`	no	The node property in the GDS graph to which the community ID is written.
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.
maxIterations	Integer	`10`	yes	The maximum number of iterations to run.
nodeWeightProperty	String	`null`	yes	The name of a node property that contains node weights.
relationshipWeightProperty	String	`null`	yes	Name of the relationship property to use as weights. If unspecified, the algorithm runs unweighted.
seedProperty	String	`n/a`	yes	The name of a node property that defines an initial numeric label.
consecutiveIds	Boolean	`false`	yes	Flag to decide whether component identifiers are mapped into a consecutive id space (requires additional memory).

Table 9. Results
Name	Type	Description
preProcessingMillis	Integer	Milliseconds for preprocessing the data.
computeMillis	Integer	Milliseconds for running the algorithm.
mutateMillis	Integer	Milliseconds for adding properties to the in-memory graph.
postProcessingMillis	Integer	Milliseconds for computing percentiles and community count.
nodePropertiesWritten	Integer	The number of node properties written.
communityCount	Integer	The number of communities found.
ranIterations	Integer	The number of iterations that were executed.
didConverge	Boolean	True if the algorithm did converge to a stable labelling within the provided number of maximum iterations.
communityDistribution	Map	Map containing min, max, mean as well as p1, p5, p10, p25, p50, p75, p90, p95, p99 and p999 percentile values of community size.
configuration	Map	The configuration used for running the algorithm.

Run Label Propagation in write mode on a named graph.

CALL gds.labelPropagation.write(
  graphName: String,
  configuration: Map
)
YIELD
  preProcessingMillis: Integer,
  computeMillis: Integer,
  writeMillis: Integer,
  postProcessingMillis: Integer,
  nodePropertiesWritten: Integer,
  communityCount: Integer,
  ranIterations: Integer,
  didConverge: Boolean,
  communityDistribution: Map,
  configuration: Map

Table 10. 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 11. 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.
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 community ID is written.
maxIterations	Integer	`10`	yes	The maximum number of iterations to run.
nodeWeightProperty	String	`null`	yes	The name of a node property that contains node weights.
relationshipWeightProperty	String	`null`	yes	Name of the relationship property to use as weights. If unspecified, the algorithm runs unweighted.
seedProperty	String	`n/a`	yes	The name of a node property that defines an initial numeric label.
consecutiveIds	Boolean	`false`	yes	Flag to decide whether component identifiers are mapped into a consecutive id space (requires additional memory).
minCommunitySize	Integer	`0`	yes	Only community ids of communities with a size greater than or equal to the given value are written to Neo4j.

Table 12. Results
Name	Type	Description
preProcessingMillis	Integer	Milliseconds for preprocessing the data.
computeMillis	Integer	Milliseconds for running the algorithm.
writeMillis	Integer	Milliseconds for writing result data back.
postProcessingMillis	Integer	Milliseconds for computing percentiles and community count.
nodePropertiesWritten	Integer	The number of node properties written.
communityCount	Integer	The number of communities found.
ranIterations	Integer	The number of iterations that were executed.
didConverge	Boolean	True if the algorithm did converge to a stable labelling within the provided number of maximum iterations.
communityDistribution	Map	Map containing min, max, mean as well as p1, p5, p10, p25, p50, p75, p90, p95, p99 and p999 percentile values of community size.
configuration	Map	The configuration used for running the algorithm.

Examples

All the examples below should be run in an empty database.

The examples use Cypher projections as the norm. Native projections will be deprecated in a future release.

In this section we will show examples of running the Label Propagation algorithm on a concrete graph. The intention is to illustrate what the results look like and to provide a guide in how to make use of the algorithm in a real setting. We will do this on a small social network graph of a handful nodes connected in a particular pattern. The example graph looks like this:

The following Cypher statement will create the example graph in the Neo4j database:

CREATE
  (alice:User {name: 'Alice', posts: 4, seed_label: 52}),
  (bridget:User {name: 'Bridget', posts: 13, seed_label: 21}),
  (charles:User {name: 'Charles', posts: 55, seed_label: 43}),
  (doug:User {name: 'Doug', posts: 5, seed_label: 21}),
  (mark:User {name: 'Mark', posts: 7, seed_label: 19}),
  (michael:User {name: 'Michael', posts: 15, seed_label: 52}),

  (alice)-[:FOLLOW {weight: 1}]->(bridget),
  (alice)-[:FOLLOW {weight: 10}]->(charles),
  (mark)-[:FOLLOW {weight: 1}]->(doug),
  (bridget)-[:FOLLOW {weight: 1}]->(michael),
  (doug)-[:FOLLOW {weight: 1}]->(mark),
  (michael)-[:FOLLOW {weight: 1}]->(alice),
  (alice)-[:FOLLOW {weight: 1}]->(michael),
  (bridget)-[:FOLLOW {weight: 1}]->(alice),
  (michael)-[:FOLLOW {weight: 1}]->(bridget),
  (charles)-[:FOLLOW {weight: 1}]->(doug)

This graph represents six users, some of whom follow each other. Besides a name property, each user also has a seed_label property. The seed_label property represents a value in the graph used to seed the node with a label. For example, this can be a result from a previous run of the Label Propagation algorithm. In addition, each relationship has a weight property.

The following statement will project a graph using a Cypher projection and store it in the graph catalog under the name 'myGraph'.

MATCH (source:User)-[r:FOLLOW]->(target:User)
RETURN gds.graph.project(
  'myGraph',
  source,
  target,
  {
    sourceNodeProperties: source { .posts, .seed_label },
    targetNodeProperties: target { .posts, .seed_label },
    relationshipProperties: r { .weight }
  }
)

In the following examples we will demonstrate using the Label Propagation algorithm on this graph.

Memory Estimation

First off, we will estimate the cost of running the algorithm using the estimate procedure. This can be done with any execution mode. We will use the write mode in this example. Estimating the algorithm is useful to understand the memory impact that running the algorithm on your graph will have. When you later actually run the algorithm in one of the execution modes the system will perform an estimation. If the estimation shows that there is a very high probability of the execution going over its memory limitations, the execution is prohibited. To read more about this, see Automatic estimation and execution blocking.

For more details on estimate in general, see Memory Estimation.

The following will estimate the memory requirements for running the algorithm in write mode:

CALL gds.labelPropagation.write.estimate('myGraph', { writeProperty: 'community' })
YIELD nodeCount, relationshipCount, bytesMin, bytesMax, requiredMemory

Table 13. Results
nodeCount	relationshipCount	bytesMin	bytesMax	requiredMemory
6	10	1592	1592	"1592 Bytes"

Stream

In the stream execution mode, the algorithm returns the community ID for each node. This allows us to inspect the results directly or post-process them in Cypher without any side effects. For example, we can order the results to see the nodes that belong to the same communities displayed next to each other.

For more details on the stream mode in general, see Stream.

The following will run the algorithm and stream results:

CALL gds.labelPropagation.stream('myGraph')
YIELD nodeId, communityId AS Community
RETURN gds.util.asNode(nodeId).name AS Name, Community
ORDER BY Community, Name

Table 14. Results
Name	Community
"Alice"	0
"Bridget"	0
"Michael"	0
"Charles"	4
"Doug"	4
"Mark"	4

In the above example we can see that our graph has two communities each containing three nodes. The default behaviour of the algorithm is to run unweighted, e.g. without using node or relationship weights. The weighted option will be demonstrated in Weighted

Stats

In the stats execution mode, the algorithm returns a single row containing a summary of the algorithm result. This execution mode does not have any side effects. It can be useful for evaluating algorithm performance by inspecting the computeMillis return item. In the examples below we will omit returning the timings. The full signature of the procedure can be found in the syntax section.

For more details on the stats mode in general, see Stats.

The following will run the algorithm in stats mode:

CALL gds.labelPropagation.stats('myGraph')
YIELD communityCount, ranIterations, didConverge

Table 15. Results
communityCount	ranIterations	didConverge
2	3	true

As we can see from the example above the algorithm finds two communities and converges in three iterations. Note that we ran the algorithm unweighted.

Mutate

The mutate execution mode extends the stats mode with an important side effect: updating the named graph with a new node property containing the community ID for that node. The name of the new property is specified using the mandatory configuration parameter mutateProperty. The result is a single summary row, similar to stats, but with some additional metrics. The mutate mode is especially useful when multiple algorithms are used in conjunction.

For more details on the mutate mode in general, see Mutate.

The following will run the algorithm and write back results:

CALL gds.labelPropagation.mutate('myGraph', { mutateProperty: 'community' })
YIELD communityCount, ranIterations, didConverge

Table 16. Results
communityCount	ranIterations	didConverge
2	3	true

The returned result is the same as in the stats example. Additionally, the graph 'myGraph' now has a node property community which stores the community ID for each node. To find out how to inspect the new schema of the in-memory graph, see Listing graphs.

Write

The write execution mode extends the stats mode with an important side effect: writing the community ID for each node as a property to the Neo4j database. The name of the new property is specified using the mandatory configuration parameter writeProperty. The result is a single summary row, similar to stats, but with some additional metrics. The write mode enables directly persisting the results to the database.

For more details on the write mode in general, see Write.

The following will run the algorithm and write back results:

CALL gds.labelPropagation.write('myGraph', { writeProperty: 'community' })
YIELD communityCount, ranIterations, didConverge

Table 17. Results
communityCount	ranIterations	didConverge
2	3	true

The returned result is the same as in the stats example. Additionally, each of the six nodes now has a new property community in the Neo4j database, containing the community ID for that node.

Weighted

When we projected myGraph, we also projected the relationship property weight. In order to tell the algorithm to consider this property as a relationship weight, we have to set the relationshipWeightProperty configuration parameter to weight.

The following will run the algorithm on a graph with weighted relationships and stream results:

CALL gds.labelPropagation.stream('myGraph', { relationshipWeightProperty: 'weight' })
YIELD nodeId, communityId AS Community
RETURN gds.util.asNode(nodeId).name AS Name, Community
ORDER BY Community, Name

Table 18. Results
Name	Community
"Bridget"	0
"Michael"	0
"Alice"	4
"Charles"	4
"Doug"	4
"Mark"	4

Compared to the unweighted run of the algorithm we still have two communities, but they contain two and four nodes respectively. Using the weighted relationships, the nodes Alice and Charles are now in the same community as there is a strong link between them.

Weighted nodes

By specifying a node weight via the nodeWeightProperty key, we can also control the influence of a nodes community onto its neighbors. During the computation of the weight of a specific community, the node property will be multiplied by the weight of that node’s relationships.

The following will run the algorithm on a graph with weighted nodes and stream results:

CALL gds.labelPropagation.stream('myGraph', { nodeWeightProperty: 'posts' })
YIELD nodeId, communityId AS Community
RETURN gds.util.asNode(nodeId).name AS Name, Community
ORDER BY Community, Name

Table 19. Results
Name	Community
"Alice"	4
"Charles"	4
"Doug"	4
"Mark"	4
"Bridget"	5
"Michael"	5

We have used the stream mode to demonstrate running the algorithm using weights, the configuration parameters are available for all the modes of the algorithm.

Seeded communities

At the beginning of the algorithm computation, every node is initialized with a unique label, and the labels propagate through the network.

An initial set of labels can be provided by setting the seedProperty configuration parameter. When we projected myGraph, we also projected the node property seed_label. We can use this node property as seedProperty.

The algorithm first checks if there is a seed label assigned to the node. If no seed label is present, the algorithm assigns new unique label to the node. Using this preliminary set of labels, it then sequentially updates each node’s label to a new one, which is the most frequent label among its neighbors at every iteration of label propagation.

The consecutiveIds configuration option cannot be used in combination with seedProperty in order to retain the seeding values.

The following will run the algorithm with pre-defined labels:

CALL gds.labelPropagation.stream('myGraph', { seedProperty: 'seed_label' })
YIELD nodeId, communityId AS Community
RETURN gds.util.asNode(nodeId).name AS Name, Community
ORDER BY Community, Name

Table 20. Results
Name	Community
"Charles"	19
"Doug"	19
"Mark"	19
"Alice"	52
"Bridget"	52
"Michael"	52

As we can see, the communities are based on the seed_label property, concretely 19 is from the node Mark and 52 from Alice.

We have used the stream mode to demonstrate running the algorithm using seedProperty, this configuration parameter is available for all the modes of the algorithm.