K-1 Coloring

Directed

Undirected

Heterogeneous nodes

Heterogeneous relationships

Weighted relationships

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 K-1 Coloring algorithm assigns a color to every node in the graph, trying to optimize for two objectives:

To make sure that every neighbor of a given node has a different color than the node itself.
To use as few colors as possible.

Note that the graph coloring problem is proven to be NP-complete, which makes it intractable on anything but trivial graph sizes. For that reason the implemented algorithm is a greedy algorithm. Thus it is neither guaranteed that the result is an optimal solution, using as few colors as theoretically possible, nor does it always produce a correct result where no two neighboring nodes have different colors. However the precision of the latter can be controlled by the number of iterations this algorithm runs.

For more information on this algorithm, see:

Running this algorithm requires sufficient memory availability. Before running this algorithm, we recommend that you read Memory Estimation.

Syntax

K-1 Coloring syntax per mode

The following describes the API for running the algorithm and stream results:

CALL gds.k1coloring.stream(graphName: String, configuration: Map)
YIELD nodeId, color

Table 1. Parameters
Name	Type	Default	Optional	Description
graphName	String	`null`	yes	The name of an existing graph on which to run the algorithm. If no graph name is provided, the configuration map must contain configuration for creating a graph.
configuration	Map	`{}`	yes	Additional configuration, see below.

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 ^[1]`	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 of K1 Coloring to run.
minCommunitySize	Integer	`0`	yes	Only nodes inside communities larger or equal the given value are returned.
1. In a GDS Session the default is the number of available processors

Table 3. Results
Name	Type	Description
nodeId	Integer	The ID of the Node
color	Integer	The color of the Node

The following describes the API for running the algorithm and returning the computation statistics:

CALL gds.k1coloring.stats(
    graphName: String,
    configuration: Map
)
YIELD
    nodeCount,
    colorCount,
    ranIterations,
    didConverge,
    configuration,
    preProcessingMillis,
    computeMillis

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
concurrency	Integer	4 ^[2]	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 of K1 Coloring to run.
2. In a GDS Session the default is the number of available processors

Table 6. Results
Name	Type	Description
nodeCount	Integer	The number of nodes considered.
ranIterations	Integer	The actual number of iterations the algorithm ran.
didConverge	Boolean	An indicator of whether the algorithm found a correct coloring.
colorCount	Integer	The number of colors used.
preProcessingMillis	Integer	Milliseconds for preprocessing the data.
computeMillis	Integer	Milliseconds for running the algorithm.
configuration	Map	The configuration used for running the algorithm.

The following describes the API for running the algorithm and mutating the projected graph:

CALL gds.k1coloring.mutate(graphName: String, configuration: Map)
YIELD nodeCount, colorCount, ranIterations, didConverge, configuration, preProcessingMillis, computeMillis, mutateMillis

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.

The configuration for the mutate mode is similar to the write mode. Instead of specifying a writeProperty, we need to specify a mutateProperty. Also, specifying writeConcurrency is not possible in mutate mode.

Table 8. Results
Name	Type	Description
nodeCount	Integer	The number of nodes considered.
ranIterations	Integer	The actual number of iterations the algorithm ran.
didConverge	Boolean	An indicator of whether the algorithm found a correct coloring.
colorCount	Integer	The number of colors used.
preProcessingMillis	Integer	Milliseconds for preprocessing the data.
computeMillis	Integer	Milliseconds for running the algorithm.
mutateMillis	Integer	Milliseconds for adding properties to the projected graph.
configuration	Map	The configuration used for running the algorithm.

The following describes the API for running the algorithm and writing results back to Neo4j:

CALL gds.k1coloring.write(graphName: String, configuration: Map)
YIELD nodeCount, colorCount, ranIterations, didConverge, configuration, preProcessingMillis, computeMillis, writeMillis

Table 9. 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 10. Configuration
Name	Type	Default	Optional	Description
concurrency	Integer	4 ^[3]	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.
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 ^[3]	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.
maxIterations	Integer	10	yes	The maximum number of iterations of K1 Coloring to run.
minCommunitySize	Integer	0	yes	Only community ids of communities with a size greater than or equal to the given value are written to Neo4j.
3. In a GDS Session the default is the number of available processors

Table 11. Results
Name	Type	Description
nodeCount	Integer	The number of nodes considered.
ranIterations	Integer	The actual number of iterations the algorithm ran.
didConverge	Boolean	An indicator of whether the algorithm found a correct coloring.
colorCount	Integer	The number of colors used.
preProcessingMillis	Integer	Milliseconds for preprocessing the data.
computeMillis	Integer	Milliseconds for running the algorithm.
writeMillis	Integer	Milliseconds for writing result data back to Neo4j.
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.

Consider the graph created by the following Cypher statement:

CREATE (alice:User {name: 'Alice'}),
       (bridget:User {name: 'Bridget'}),
       (charles:User {name: 'Charles'}),
       (doug:User {name: 'Doug'}),

       (alice)-[:LINK]->(bridget),
       (alice)-[:LINK]->(charles),
       (alice)-[:LINK]->(doug),
       (bridget)-[:LINK]->(charles)

This graph has a super node with name "Alice" that connects to all other nodes. It should therefore not be possible for any other node to be assigned the same color as the Alice node.

MATCH (source:User)-[r:LINK]->(target:User)
RETURN gds.graph.project(
  'myGraph',
  source,
  target,
  {},
  { undirectedRelationshipTypes: ['*'] }
)

We can now go ahead and project a graph with all the User nodes and the LINK relationships with UNDIRECTED orientation.

The following statement will project the graph and store it in the graph catalog.

MATCH (source:Person)-[r:LIKES]->(target:Person)
RETURN gds.graph.project(
  'myGraph',
  source,
  target
)

In the following examples we will demonstrate using the K-1 Coloring algorithm on this graph.

Running the K-1 Coloring algorithm in stream mode:

CALL gds.k1coloring.stream('myGraph')
YIELD nodeId, color
RETURN gds.util.asNode(nodeId).name AS name, color
ORDER BY name

Table 12. Results
name	color
`"Alice"`	`0`
`"Bridget"`	`1`
`"Charles"`	`2`
`"Doug"`	`1`

It is also possible to write the assigned colors back to the database using the write mode.

Running the K-1 Coloring algorithm in write mode:

CALL gds.k1coloring.write('myGraph', {writeProperty: 'color'})
YIELD nodeCount, colorCount, ranIterations, didConverge

Table 13. Results
nodeCount	colorCount	ranIterations	didConverge
`4`	`3`	`1`	`true`

When using write mode the procedure will return information about the algorithm execution. In this example we return the number of processed nodes, the number of colors used to color the graph, the number of iterations and information whether the algorithm converged.

To instead mutate the in-memory graph with the assigned colors, the mutate mode can be used as follows.

Running the K-1 Coloring algorithm in mutate mode:

CALL gds.k1coloring.mutate('myGraph', {mutateProperty: 'color'})
YIELD nodeCount, colorCount, ranIterations, didConverge

Table 14. Results
nodeCount	colorCount	ranIterations	didConverge
`4`	`3`	`1`	`true`

Similar to the write mode, stats mode can run the algorithm and return only the execution statistics without persisting the results.

Running the K-1 Coloring algorithm in stats mode:

CALL gds.k1coloring.stats('myGraph')
YIELD nodeCount, colorCount, ranIterations, didConverge

Table 15. Results
nodeCount	colorCount	ranIterations	didConverge
`4`	`3`	`1`	`true`