Modularity metric

This feature is in the alpha tier. For more information on feature tiers, see Operations reference.

Supported algorithm traits:

1. Introduction

Modularity is a metric that allows you to evaluate the quality of a community detection. Relationships of nodes in a community C connect to nodes either within C or outside C. Graphs with high modularity have dense connections between the nodes within communities but sparse connections between nodes in different communities.

2. Syntax

This section covers the syntax used to execute the Modularity Metric 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.

Example 1. Modularity syntax per mode
Run Modularity in stream mode on a named graph.
CALL gds.alpha.modularity.stream(
  graphName: String,
  configuration: Map
) YIELD
  communityId: Integer,
  modularity: 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. Configuration
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.

jobId

String

Generated internally

yes

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

communityProperty

String

n/a

no

The node property that holds the community ID as an integer for each node. Note that only non-negative community IDs are considered valid and will have their conductance computed.

relationshipWeightProperty

String

null

yes

Relationship Weight.

Table 3. Results
Name Type Description

communityId

Integer

Community ID.

modularity

Float

Modularity of the community.

Run Modularity in stats mode on a named graph.
CALL gds.alpha.modularity.stats(
  graphName: String,
  configuration: Map
) YIELD
  nodeCount: Integer,
  relationshipCount: Integer,
  communityCount: Integer,
  modularity: Float,
  postProcessingMillis: Integer,
  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.

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.

communityProperty

String

n/a

no

The node property that holds the community ID as an integer for each node. Note that only non-negative community IDs are considered valid and will have their conductance computed.

relationshipWeightProperty

String

null

yes

Relationship Weight.

Table 6. Results
Name Type Description

nodeCount

Integer

The number of nodes in the graph.

relationshipCount

Integer

The number of relationships in the graph.

communityCount

Integer

The number of communities.

modularity

Float

The total modularity score.

preProcessingMillis

Integer

Milliseconds for preprocessing the data.

computeMillis

Integer

Milliseconds for running the algorithm.

postProcessingMillis

Integer

Milliseconds for computing percentiles and community count.

configuration

Map

The configuration used for running the algorithm.

3. Examples

In this section we will show examples of running the Modularity 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:

Visualization of the example graph
The following Cypher statement will create the example graph in the Neo4j database:
CREATE
  (nAlice:User {name: 'Alice', community: 3}),
  (nBridget:User {name: 'Bridget', community: 2}),
  (nCharles:User {name: 'Charles', community: 2}),
  (nDoug:User {name: 'Doug', community: 3}),
  (nMark:User {name: 'Mark', community: 5}),
  (nMichael:User {name: 'Michael', community: 5}),

  (nAlice)-[:LINK {weight: 1}]->(nBridget),
  (nAlice)-[:LINK {weight: 1}]->(nCharles),
  (nCharles)-[:LINK {weight: 1}]->(nBridget),

  (nAlice)-[:LINK {weight: 5}]->(nDoug),

  (nMark)-[:LINK {weight: 1}]->(nDoug),
  (nMark)-[:LINK {weight: 1}]->(nMichael),
  (nMichael)-[:LINK {weight: 1}]->(nMark);

This graph has three pre-computed communities of Users, that are closely connected. For more details on the available community detection algorithms, please refer to Community algorithms section of the documentation. The communities are indicated by the community node property on each node. The relationships that connect the nodes in each component have a property weight which determines the strength of the relationship.

We can now project the graph and store it in the graph catalog. We load the LINK relationships with orientation set to UNDIRECTED.

In the examples below we will use named graphs and native projections as the norm. However, Cypher projections can also be used.

The following statement will project the graph and store it in the graph catalog.
CALL gds.graph.project(
    'myGraph',
    'User',
    {
        LINK: {
            orientation: 'UNDIRECTED'
        }
    },
    {
        nodeProperties: 'community',
        relationshipProperties: 'weight'
    }
)

3.1. Stream

Since we have community information on each node, we can evaluate how good it is under the modularity metric. Note that we in this case we use the feature of relationships being weighted by a relationship property.

The Modularity stream procedure returns the modularity for each community. This allows us to inspect the results directly or post-process them in Cypher without any side effects.

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

The following will run the Modularity algorithm in stream mode:
CALL gds.alpha.modularity.stream('myGraph', { communityProperty: 'community', relationshipWeightProperty: 'weight' })
YIELD communityId, modularity
Table 7. Results
communityId modularity

2

0.057851239669421

3

0.105371900826446

5

0.130165289256198

We can see that the community of the weighted graph with the highest modularity is community 5. This means that 5 is the community that is most "well-knit" in the sense that most of its relationship weights are internal to the community.

3.2. Stats

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

The following will run the Modularity algorithm in stats mode:
CALL gds.alpha.modularity.stats('myGraph', { communityProperty: 'community', relationshipWeightProperty: 'weight' })
YIELD nodeCount, relationshipCount, communityCount, modularity
Table 8. Results
nodeCount relationshipCount communityCount modularity

6

14

3

0.293388429752066