Modularity metric
Glossary
 Directed

Directed trait. The algorithm is welldefined 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 welldefined 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
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.
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.
CALL gds.modularity.stream(
graphName: String,
configuration: Map
) YIELD
communityId: Integer,
modularity: Float
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. Nodes with any of the given labels will be included. 

List of String 

yes 
Filter the named graph using the given relationship types. Relationships with any of the given types will be included. 

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. 

Boolean 

yes 
If disabled the progress percentage will not be logged. 

String 

yes 
Name of the relationship property to use as weights. If unspecified, the algorithm runs unweighted. 

communityProperty 
String 

no 
The node property that holds the community ID as an integer for each node. Note that only nonnegative community IDs are considered valid and will have their modularity score computed. 
Name  Type  Description 

communityId 
Integer 
Community ID. 
modularity 
Float 
Modularity of the community. 
CALL gds.modularity.stats(
graphName: String,
configuration: Map
) YIELD
nodeCount: Integer,
relationshipCount: Integer,
communityCount: Integer,
modularity: Float,
postProcessingMillis: Integer,
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. Nodes with any of the given labels will be included. 

List of String 

yes 
Filter the named graph using the given relationship types. Relationships with any of the given types will be included. 

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. 

Boolean 

yes 
If disabled the progress percentage will not be logged. 

String 

yes 
Name of the relationship property to use as weights. If unspecified, the algorithm runs unweighted. 

communityProperty 
String 

no 
The node property that holds the community ID as an integer for each node. Note that only nonnegative community IDs are considered valid and will have their modularity score computed. 
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. 
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 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:
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 precomputed 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
.
MATCH (source:User)[r:LINK]>(target:User)
RETURN gds.graph.project(
'myGraph',
source,
target,
{
sourceNodeProperties: source { .community },
targetNodeProperties: target { .community },
relationshipProperties: r { .weight }
},
{ undirectedRelationshipTypes: ['*'] }
)
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 stats
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.
CALL gds.modularity.stats.estimate('myGraph', {
communityProperty: 'community',
relationshipWeightProperty: 'weight'
})
YIELD nodeCount, relationshipCount, bytesMin, bytesMax, requiredMemory
nodeCount  relationshipCount  bytesMin  bytesMax  requiredMemory 

6 
14 
872 
872 
"872 Bytes" 
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 postprocess them in Cypher without any side effects.
For more details on the stream mode in general, see Stream.
stream
mode:CALL gds.modularity.stream('myGraph', {
communityProperty: 'community',
relationshipWeightProperty: 'weight'
})
YIELD communityId, modularity
RETURN communityId, modularity
ORDER BY communityId ASC
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 "wellknit" in the sense that most of its relationship weights are internal to the community.
Stats
For more details on the stream mode in general, see Stats.
stats
mode:CALL gds.modularity.stats('myGraph', {
communityProperty: 'community',
relationshipWeightProperty: 'weight'
})
YIELD nodeCount, relationshipCount, communityCount, modularity
nodeCount  relationshipCount  communityCount  modularity 

6 
14 
3 
0.293388429752066 