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.

 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}),

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.