# K-1 Coloring

This feature is in the beta tier. For more information on feature tiers, see API Tiers.

Supported algorithm traits:

## 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.

## 1. Introduction

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

1. To make sure that every neighbor of a given node has a different color than the node itself.

2. 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.

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

## 2. Syntax

K-1 Coloring syntax per mode
The following describes the API for running the algorithm and stream results:
``````CALL gds.beta.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

Table 2. Configuration
Name Type Default Optional Description

concurrency

Integer

4

yes

The number of concurrent threads used for running the algorithm. Also provides the default value for 'readConcurrency' and 'writeConcurrency'. This is dependent on the Neo4j edition; for more information, see CPU.

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.

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.beta.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

yes

The number of concurrent threads used for running the algorithm. Also provides the default value for 'readConcurrency' and 'writeConcurrency'. This is dependent on the Neo4j edition; for more information, see CPU.

maxIterations

Integer

10

yes

The maximum number of iterations of K1 Coloring to run.

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.beta.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.beta.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

yes

The number of concurrent threads used for running the algorithm. Also provides the default value for 'readConcurrency' and 'writeConcurrency'. This is dependent on the Neo4j edition; for more information, see CPU.

writeConcurrency

Integer

value of 'concurrency'

yes

The number of concurrent threads used for writing the result.

maxIterations

Integer

10

yes

The maximum number of iterations of K1 Coloring to run.

writeProperty

String

n/a

no

The node property this procedure writes the color to.

minCommunitySize

Integer

0

yes

Only community ids of communities with a size greater than or equal to the given value are written to Neo4j.

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.

## 3. Examples

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'}),

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.

``````CALL gds.graph.project(
'myGraph',
'User',
{
orientation: 'UNDIRECTED'
}
}
)``````

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

 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', 'Person', 'LIKES')``

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.beta.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.beta.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.beta.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.beta.k1coloring.stats('myGraph')
YIELD nodeCount, colorCount, ranIterations, didConverge``````
Table 15. Results
nodeCount colorCount ranIterations didConverge

`4`

`3`

`1`

`true`