Strongly Connected Components
The Strongly Connected Components (SCC) algorithm finds maximal sets of connected nodes in a directed graph. A set is considered a strongly connected component if there is a directed path between each pair of nodes within the set. It is often used early in a graph analysis process to help us get an idea of how our graph is structured.
This feature is in the alpha tier. For more information on feature tiers, see API Tiers.
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.
1. History and explanation
SCC is one of the earliest graph algorithms, and the first lineartime algorithm was described by Tarjan in 1972. Decomposing a directed graph into its strongly connected components is a classic application of the depthfirst search algorithm.
2. Usecases  when to use the Strongly Connected Components algorithm

In the analysis of powerful transnational corporations, SCC can be used to find the set of firms in which every member owns directly and/or indirectly owns shares in every other member. Although it has benefits, such as reducing transaction costs and increasing trust, this type of structure can weaken market competition. Read more in "The Network of Global Corporate Control".

SCC can be used to compute the connectivity of different network configurations when measuring routing performance in multihop wireless networks. Read more in "Routing performance in the presence of unidirectional links in multihop wireless networks"

Strongly Connected Components algorithms can be used as a first step in many graph algorithms that work only on strongly connected graph. In social networks, a group of people are generally strongly connected (For example, students of a class or any other common place). Many people in these groups generally like some common pages, or play common games. The SCC algorithms can be used to find such groups, and suggest the commonly liked pages or games to the people in the group who have not yet liked those pages or games.
3. Syntax
Decomposition syntax per mode
CALL gds.scc.stream(graphName: String, configuration: Map)
YIELD nodeId,
componentId
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. 

consecutiveIds 
Boolean 

yes 
Flag to decide whether component identifiers are mapped into a consecutive id space (requires additional memory). 
Name  Type  Description 

nodeId 
Integer 
Node ID. 
componentId 
Integer 
Component ID. 
CALL gds.scc.stats(
graphName: string,
configuration: map
)
YIELD
componentCount: Integer,
preProcessingMillis: Integer,
computeMillis: Integer,
postProcessingMillis: Integer,
componentDistribution: Map,
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. 

consecutiveIds 
Boolean 

yes 
Flag to decide whether component identifiers are mapped into a consecutive id space (requires additional memory). 
Name  Type  Description 

componentCount 
Integer 
The number of computed strongly connected components. 
preProcessingMillis 
Integer 
Milliseconds for preprocessing the data. 
computeMillis 
Integer 
Milliseconds for running the algorithm. 
postProcessingMillis 
Integer 
Milliseconds for computing component count and distribution statistics. 
componentDistribution 
Map 
Map containing min, max, mean as well as p1, p5, p10, p25, p50, p75, p90, p95, p99 and p999 percentile values of component sizes. 
configuration 
Map 
The configuration used for running the algorithm. 
CALL gds.scc.mutate(
graphName: string,
configuration: map
)
YIELD
componentCount: Integer,
nodePropertiesWritten: Integer,
preProcessingMillis: Integer,
computeMillis: Integer,
mutateMillis: Integer,
postProcessingMillis: Integer,
componentDistribution: Map,
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 

mutateProperty 
String 

no 
The node property in the GDS graph to which the component is written. 
List of String 

yes 
Filter the named graph using the given node labels. 

List of String 

yes 
Filter the named graph using the given relationship types. 

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. 

consecutiveIds 
Boolean 

yes 
Flag to decide whether component identifiers are mapped into a consecutive id space (requires additional memory). 
Name  Type  Description 

componentCount 
Integer 
The number of computed strongly connected components. 
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 mutating the inmemory graph. 
postProcessingMillis 
Integer 
Milliseconds for computing component count and distribution statistics. 
componentDistribution 
Map 
Map containing min, max, mean as well as p1, p5, p10, p25, p50, p75, p90, p95, p99 and p999 percentile values of component sizes. 
configuration 
Map 
The configuration used for running the algorithm. 
CALL gds.scc.write(
graphName: string,
configuration: map
)
YIELD
componentCount: Integer,
nodePropertiesWritten: Integer,
preProcessingMillis: Integer,
computeMillis: Integer,
writeMillis: Integer,
postProcessingMillis: Integer,
componentDistribution: Map,
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. 

Integer 

yes 
The number of concurrent threads used for writing the result to Neo4j. 

String 

no 
The node property in the Neo4j database to which the component is written. 

consecutiveIds 
Boolean 

yes 
Flag to decide whether component identifiers are mapped into a consecutive id space (requires additional memory). 
Name  Type  Description 

componentCount 
Integer 
The number of computed strongly connected components. 
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 back to Neo4j. 
postProcessingMillis 
Integer 
Milliseconds for computing component count and distribution statistics. 
componentDistribution 
Map 
Map containing min, max, mean as well as p1, p5, p10, p25, p50, p75, p90, p95, p99 and p999 percentile values of component sizes. 
configuration 
Map 
The configuration used for running the algorithm. 
4. Strongly Connected Components algorithm examples
CREATE (nAlice:User {name:'Alice'})
CREATE (nBridget:User {name:'Bridget'})
CREATE (nCharles:User {name:'Charles'})
CREATE (nDoug:User {name:'Doug'})
CREATE (nMark:User {name:'Mark'})
CREATE (nMichael:User {name:'Michael'})
CREATE (nAlice)[:FOLLOW]>(nBridget)
CREATE (nAlice)[:FOLLOW]>(nCharles)
CREATE (nMark)[:FOLLOW]>(nDoug)
CREATE (nMark)[:FOLLOW]>(nMichael)
CREATE (nBridget)[:FOLLOW]>(nMichael)
CREATE (nDoug)[:FOLLOW]>(nMark)
CREATE (nMichael)[:FOLLOW]>(nAlice)
CREATE (nAlice)[:FOLLOW]>(nMichael)
CREATE (nBridget)[:FOLLOW]>(nAlice)
CREATE (nMichael)[:FOLLOW]>(nBridget);
CALL gds.graph.project('graph', 'User', 'FOLLOW')
4.1. 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.
CALL gds.scc.write.estimate('graph', { writeProperty: 'componentId' })
YIELD nodeCount, relationshipCount, bytesMin, bytesMax, requiredMemory
nodeCount  relationshipCount  bytesMin  bytesMax  requiredMemory 

6 
10 
33332 
33332 
"32 KiB" 
4.2. Stream
In the stream
execution mode, the algorithm returns the component for each node.
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.
CALL gds.scc.stream('graph', {})
YIELD nodeId, componentId
RETURN gds.util.asNode(nodeId).name AS Name, componentId AS Component
ORDER BY Component DESC
Name  Component 













We have 3 strongly connected components in our sample graph.
The first, and biggest, component has members Alice, Bridget, and Michael, while the second component has Doug and Mark. Charles ends up in his own component because there isn’t an outgoing relationship from that node to any of the others.
4.3. 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.
CALL gds.scc.stats('graph')
YIELD componentCount
componentCount 

3 
4.4. 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 component 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.
graph
:CALL gds.scc.mutate('graph', { mutateProperty: 'componentId'})
YIELD componentCount
componentCount 

3 
4.5. Write
The write
execution mode extends the stats
mode with an important side effect: writing the component 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.
CALL gds.scc.write('graph', {
writeProperty: 'componentId'
})
YIELD componentCount, componentDistribution
RETURN componentCount,componentDistribution.max as maxSetSize, componentDistribution.min as minSetSize
componentCount  maxSetSize  minSetSize 




MATCH (u:User)
RETURN u.componentId AS Component, count(*) AS ComponentSize
ORDER BY ComponentSize DESC
LIMIT 1
Component  ComponentSize 


