Articulation Points

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

Given a graph, an articulation point is a node whose removal increases the number of connected components in the graph. The Neo4j GDS Library provides an efficient linear time sequential algorithm to compute all articulation points in a graph.

Syntax

This section covers the syntax used to execute the Articulation Points 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.

Articulation Points syntax per mode

Run Articulation points in stream mode on a named graph.

CALL gds.articulationPoints.stream(
  graphName: String,
  configuration: Map
)
YIELD
  nodeId: 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	`1`	yes	The algorithm is single-threaded and changing the concurrency parameter has no effect on the runtime.
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.

Table 3. Results
Name	Type	Description
nodeId	Integer	The ID of the node representing an articulation point.

Run Articulation points in stats mode on a named graph.

CALL gds.articulationPoints.stats(
  graphName: String,
  configuration: Map
)
YIELD
  nodeId: Integer

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	`1`	yes	The algorithm is single-threaded and changing the concurrency parameter has no effect on the runtime.
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.

Table 6. Results
Name	Type	Description
Name	Type	Description
computeMillis	Integer	Milliseconds for running the algorithm.
articulationPointCount	Integer	Count of the articulation points in the graph.
configuration	Map	The configuration used for running the algorithm.

Run Articulation points in mutate mode on a named graph.

CALL gds.articulationPoints.mutate(
  graphName: String,
  configuration: Map
)
YIELD
  mutateMillis: Integer,
  nodePropertiesWritten: Integer,
  computeMillis: Integer,
  articulationPointCount: Integer,
  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 node property 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.

Table 9. Results
Name	Type	Description
mutateMillis	Integer	Milliseconds for adding properties to the projected graph.
nodePropertiesWritten	Integer	Number of properties added to the projected graph.
computeMillis	Integer	Milliseconds for running the algorithm.
articulationPointCount	Integer	Count of the articulation points in the graph.
configuration	Map	The configuration used for running the algorithm.

Run Articulation points in write mode on a named graph.

CALL gds.articulationPoints.write(
  graphName: String,
  configuration: Map
)
YIELD
  writeMillis: Integer,
  nodePropertiesWritten: Integer,
  computeMillis: Integer,
  articulationPointCount: Integer,
  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	`1`	yes	The algorithm is single-threaded and changing the concurrency parameter has no effect on the runtime.
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 node property is written.

Table 12. Results
Name	Type	Description
writeMillis	Integer	Milliseconds for adding properties to the neo4j database.
nodePropertiesWritten	Integer	Number of properties added to the neo4j database..
computeMillis	Integer	Milliseconds for running the algorithm.
articulationPointCount	Integer	Count of the articulation points in the graph.
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 Articulation Points 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
  (nAlice:User {name: 'Alice'}),
  (nBridget:User {name: 'Bridget'}),
  (nCharles:User {name: 'Charles'}),
  (nDoug:User {name: 'Doug'}),
  (nMark:User {name: 'Mark'}),
  (nMichael:User {name: 'Michael'}),

  (nAlice)-[:LINK]->(nBridget),
  (nAlice)-[:LINK]->(nCharles),
  (nCharles)-[:LINK]->(nBridget),

  (nAlice)-[:LINK]->(nDoug),

  (nMark)-[:LINK]->(nDoug),
  (nMark)-[:LINK]->(nMichael),
  (nMichael)-[:LINK]->(nDoug);

This graph has two clusters of Users, that are closely connected. Between those clusters there is one single edge.

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:LINK]->(target:User)
RETURN gds.graph.project(
  'myGraph',
  source,
  target,
  {},
  { 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 stream 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:

CALL gds.articulationPoints.stream.estimate('myGraph', {})
YIELD nodeCount, relationshipCount, bytesMin, bytesMax, requiredMemory

Table 13. Results
nodeCount	relationshipCount	bytesMin	bytesMax	requiredMemory
6	14	984	984	"984 Bytes"

Stream

In the stream execution mode, the algorithm returns the node property for each node. 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 algorithm in stream mode:

CALL gds.articulationPoints.stream('myGraph')
YIELD nodeId
RETURN gds.util.asNode(nodeId).name AS name
ORDER BY name ASC

Table 14. Results
name
"Alice"
"Doug"

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.articulationPoints.stats('myGraph',{})
YIELD articulationPointCount

Table 15. Results
articulationPointCount
2

Mutate

The mutate mode updates the named graph with a new node property that denotes whether a node is an articulation point or not. This is achieved through setting 0,1 values, where 1 denotes that the node is an articulation point. 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 following will run the algorithm in mutate mode:

CALL gds.articulationPoints.mutate('myGraph', { mutateProperty: 'articulationPoint'})
YIELD articulationPointCount

Table 16. Results
articulationPointCount
2

Write

The write mode updates the Neo4j graph with a new node property that denotes whether a node is an articulation point or not. This is achieved through setting 0,1 values, where 1 denotes that the node is an articulation point. 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 mutate mode is especially useful when multiple algorithms are used in conjunction.

The following will run the algorithm in write mode:

CALL gds.articulationPoints.write('myGraph', { writeProperty: 'articulationPoint'})
YIELD articulationPointCount

Table 17. Results
articulationPointCount
2

Then we can then query Neo4j to see the articulation points:

MATCH (n { articulationPoint: 1 }) RETURN n.name AS name ORDER BY name ASC

Table 18. Results
name
"Alice"
"Doug"

Or we can query Neo4j to see the nodes that are not articulation points:

MATCH (n { articulationPoint: 0 }) RETURN n.name AS name ORDER BY name ASC

Table 19. Results
name
"Bridget"
"Charles"
"Mark"
"Michael"