KMeans Clustering
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
KMeans clustering is an unsupervised learning algorithm that is used to solve clustering problems.
It follows a simple procedure of classifying a given data set into a number of clusters, defined by the parameter k
.
The Neo4j GDS Library conducts clustering based on node properties, with a float array node property being passed as input via the nodeProperty
parameter.
Nodes in the graph are then positioned as points in a d
dimensional space (where d
is the length of the array property).
The algorithm then begins by selecting k
initial cluster centroids, which are d
dimensional arrays (see section below for more details).
The centroids act as representatives for a cluster.
Then, all nodes in the graph calculate their Euclidean distance from each of the cluster centroids and are assigned to the cluster of minimum distance from them.
After these assignments, each cluster takes the mean of all nodes (as points) assigned to it to form its new representative centroid (as a d
dimensional array).
The process repeats with the new centroids until results stabilize, i.e., only a few nodes change clusters per iteration or the number of maximum iterations is reached.
Note that the KMeans implementation ignores relationships as it is only focused on node properties.
For more information on this algorithm, see:
Initial Centroid Sampling
The algorithm starts by picking k
centroids by randomly sampling from the set of available nodes.
There are two different sampling strategies.
 Uniform

With uniform sampling, each node has the same probability to be picked as one of the
k
initial centroids. This is the default sampler for KMeans denoted with theuniform
parameter.  KMeans++

This sampling strategy adapts the wellknown Kmeans++ initialization algorithm^{[1]} for KMeans. The sampling begins by choosing the first centroid uniformly at random. Then, the remaining
k1
centroids are picked onebyone based on weighted random sampling. That is, the probability a node is chosen as the next centroid is proportional to its minimum distance from the already picked centroids. Nodes with larger distance hence have higher chance to be picked as a centroid. This sampling strategy tries to spread the initial clusters more evenly so as to obtain a better final clustering. This option can be enabled by choosingkmeans++
as the initial sampler in the configuration.
It is also possible to explicitly give the list of initial centroids to the algorithm via the seedCentroids
parameter. In this case, the value of the initialSampler
parameter is ignored, even if changed in the configuration.
Considerations
In order for KMeans to work properly, the property arrays for all nodes must have the same number of elements. Also, they should contain exclusively numbers and not contain any NaN values.
Syntax
CALL gds.kmeans.stream(
graphName: String,
configuration: Map
)
YIELD
nodeId: Integer,
communityId: Integer,
distanceFromCentroid: Float,
silhouette: 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. 

nodeProperty 
String 

no 
A node property corresponding to an array of floats used by KMeans to cluster nodes into communities. 
k 
Integer 

yes 
Number of desired clusters. 
maxIterations 
Integer 

yes 
The maximum number of iterations of KMeans to run. 
deltaThreshold 
Float 

yes 
Value as a percentage to determine when to stop early. If fewer than 'deltaThreshold * nodes' nodes change their cluster , the algorithm stops. Value must be between 0 (exclusive) and 1 (inclusive). 
numberOfRestarts 
Integer 

yes 
Number of times to execute KMeans with different initial centers. The communities returned are those minimizing the average nodecenter distances. 
randomSeed 
Integer 

yes 
The seed value to control the initial centroid assignment. 
String 

yes 
The method used to sample the first 

seedCentroids 
List of List of Float 

yes 
Parameter to explicitly give the initial centroids. It cannot be enabled together with a nondefault value of the 
computeSilhouette 
Boolean 

yes 
If set to true, the silhouette scores are computed once the clustering has been determined. Silhouette is a metric on how well the nodes have been clustered. 
Name  Type  Description 

nodeId 
Integer 
Node ID. 
communityId 
Integer 
The community ID. 
distanceFromCentroid 
Float 
Distance of the node from the centroid of its community. 
silhouette 
Float 
Silhouette score of the node. 
CALL gds.kmeans.stats(
graphName: String,
configuration: Map
)
YIELD
preProcessingMillis: Integer,
computeMillis: Integer,
postProcessingMillis: Integer,
communityDistribution: Map,
centroids: List of List of Float,
averageDistanceToCentroid: Float,
averageSilhouette: Float,
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. 

nodeProperty 
String 

no 
A node property corresponding to an array of floats used by KMeans to cluster nodes into communities. 
k 
Integer 

yes 
Number of desired clusters. 
maxIterations 
Integer 

yes 
The maximum number of iterations of KMeans to run. 
deltaThreshold 
Float 

yes 
Value as a percentage to determine when to stop early. If fewer than 'deltaThreshold * nodes' nodes change their cluster , the algorithm stops. Value must be between 0 (exclusive) and 1 (inclusive). 
numberOfRestarts 
Integer 

yes 
Number of times to execute KMeans with different initial centers. The communities returned are those minimizing the average nodecenter distances. 
randomSeed 
Integer 

yes 
The seed value to control the initial centroid assignment. 
String 

yes 
The method used to sample the first 

seedCentroids 
List of List of Float 

yes 
Parameter to explicitly give the initial centroids. It cannot be enabled together with a nondefault value of the 
computeSilhouette 
Boolean 

yes 
If set to true, the silhouette scores are computed once the clustering has been determined. Silhouette is a metric on how well the nodes have been clustered. 
Name  Type  Description 

preProcessingMillis 
Integer 
Milliseconds for preprocessing the data. 
computeMillis 
Integer 
Milliseconds for running the algorithm. 
postProcessingMillis 
Integer 
Milliseconds for computing percentiles and community count. 
communityDistribution 
Map 
Map containing min, max, mean as well as p1, p5, p10, p25, p50, p75, p90, p95, p99 and p999 percentile values of community size for the last level. 
centroids 
List of List of Float 
List of centroid coordinates. Each item is a list containing the coordinates of one centroid. 
averageDistanceToCentroid 
Float 
Average distance between node and centroid. 
averageSilhouette 
Float 
Average silhouette score over all nodes. 
configuration 
Map 
The configuration used for running the algorithm. 
CALL gds.kmeans.mutate(
graphName: String,
configuration: Map
)
YIELD
preProcessingMillis: Integer,
computeMillis: Integer,
mutateMillis: Integer,
postProcessingMillis: Integer,
nodePropertiesWritten: Integer,
communityDistribution: Map,
centroids: List of List of Float,
averageDistanceToCentroid: Float,
averageSilhouette: Float,
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 cluster 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. 

nodeProperty 
String 

no 
A node property corresponding to an array of floats used by KMeans to cluster nodes into communities. 
k 
Integer 

yes 
Number of desired clusters. 
maxIterations 
Integer 

yes 
The maximum number of iterations of KMeans to run. 
deltaThreshold 
Float 

yes 
Value as a percentage to determine when to stop early. If fewer than 'deltaThreshold * nodes' nodes change their cluster , the algorithm stops. Value must be between 0 (exclusive) and 1 (inclusive). 
numberOfRestarts 
Integer 

yes 
Number of times to execute KMeans with different initial centers. The communities returned are those minimizing the average nodecenter distances. 
randomSeed 
Integer 

yes 
The seed value to control the initial centroid assignment. 
String 

yes 
The method used to sample the first 

seedCentroids 
List of List of Float 

yes 
Parameter to explicitly give the initial centroids. It cannot be enabled together with a nondefault value of the 
computeSilhouette 
Boolean 

yes 
If set to true, the silhouette scores are computed once the clustering has been determined. Silhouette is a metric on how well the nodes have been clustered. 
Name  Type  Description 

preProcessingMillis 
Integer 
Milliseconds for preprocessing the data. 
computeMillis 
Integer 
Milliseconds for running the algorithm. 
mutateMillis 
Integer 
Milliseconds for adding properties to the projected graph. 
postProcessingMillis 
Integer 
Milliseconds for computing percentiles and community count. 
nodePropertiesWritten 
Integer 
Number of properties added to the projected graph. 
communityDistribution 
Map 
Map containing min, max, mean as well as p1, p5, p10, p25, p50, p75, p90, p95, p99 and p999 percentile values of community size for the last level. 
centroids 
List of List of Float 
List of centroid coordinates. Each item is a list containing the coordinates of one centroid. 
averageDistanceToCentroid 
Float 
Average distance between node and centroid. 
averageSilhouette 
Float 
Average silhouette score over all nodes. 
configuration 
Map 
The configuration used for running the algorithm. 
CALL gds.kmeans.write(
graphName: String,
configuration: Map
)
YIELD
preProcessingMillis: Integer,
computeMillis: Integer,
writeMillis: Integer,
postProcessingMillis: Integer,
nodePropertiesWritten: Integer,
communityDistribution: Map,
centroids: List of List of Float,
averageDistanceToCentroid: Float,
averageSilhouette: Float,
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 cluster is written. 

nodeProperty 
String 

no 
A node property corresponding to an array of floats used by KMeans to cluster nodes into communities. 
k 
Integer 

yes 
Number of desired clusters. 
maxIterations 
Integer 

yes 
The maximum number of iterations of KMeans to run. 
deltaThreshold 
Float 

yes 
Value as a percentage to determine when to stop early. If fewer than 'deltaThreshold * nodes' nodes change their cluster , the algorithm stops. Value must be between 0 (exclusive) and 1 (inclusive). 
numberOfRestarts 
Integer 

yes 
Number of times to execute KMeans with different initial centers. The communities returned are those minimizing the average nodecenter distances. 
randomSeed 
Integer 

yes 
The seed value to control the initial centroid assignment. 
String 

yes 
The method used to sample the first 

seedCentroids 
List of List of Float 

yes 
Parameter to explicitly give the initial centroids. It cannot be enabled together with a nondefault value of the 
computeSilhouette 
Boolean 

yes 
If set to true, the silhouette scores are computed once the clustering has been determined. Silhouette is a metric on how well the nodes have been clustered. 
Name  Type  Description 

preProcessingMillis 
Integer 
Milliseconds for preprocessing the data. 
computeMillis 
Integer 
Milliseconds for running the algorithm. 
writeMillis 
Integer 
Milliseconds for adding properties to the Neo4j database. 
postProcessingMillis 
Integer 
Milliseconds for computing percentiles and community count. 
nodePropertiesWritten 
Integer 
Number of properties added to the projected graph. 
communityDistribution 
Map 
Map containing min, max, mean as well as p1, p5, p10, p25, p50, p75, p90, p95, p99 and p999 percentile values of community size for the last level. 
centroids 
List of List of Float 
List of centroid coordinates. Each item is a list containing the coordinates of one centroid. 
averageDistanceToCentroid 
Float 
Average distance between node and centroid. 
averageSilhouette 
Float 
Average silhouette score over all nodes. 
configuration 
Map 
The configuration used for running the algorithm. 
Examples
All the examples below should be run in an empty database. The examples use native projections as the norm, although Cypher projections can be used as well. 
In this section we will show examples of running the KMeans 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 cities graph of a handful nodes connected in a particular pattern. The example graph looks like this:
CREATE
(:City {name: 'Surbiton', coordinates: [51.39148, 0.29825]}),
(:City {name: 'Liverpool', coordinates: [53.41058, 2.97794]}),
(:City {name: 'Kingston upon Thames', coordinates: [51.41259, 0.2974]}),
(:City {name: 'Sliven', coordinates: [42.68583, 26.32917]}),
(:City {name: 'Solna', coordinates: [59.36004, 18.00086]}),
(:City {name: 'Örkelljunga', coordinates: [56.28338, 13.27773]}),
(:City {name: 'Malmö', coordinates: [55.60587, 13.00073]}),
(:City {name: 'Xánthi', coordinates: [41.13488, 24.888]});
This graph is composed of various City nodes, in three global locations  United Kingdom, Sweden and the Balkan region in Europe.
We can now project the graph and store it in the graph catalog.
We load the City
node label with coordinates
node property.
CALL gds.graph.project(
'cities',
{
City: {
properties: 'coordinates'
}
},
'*'
)
In the following examples we will demonstrate using the KMeans algorithm on this graph to find communities of cities that are close to each other geographically.
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.kmeans.write.estimate('cities', {
writeProperty: 'kmeans',
nodeProperty: 'coordinates'
})
YIELD nodeCount, bytesMin, bytesMax, requiredMemory
nodeCount  bytesMin  bytesMax  requiredMemory 

8 
33272 
54264 
"[32 KiB ... 52 KiB]" 
Stream
In the stream
execution mode, the algorithm returns the cluster 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.kmeans.stream('cities', {
nodeProperty: 'coordinates',
k: 3,
randomSeed: 42
})
YIELD nodeId, communityId
RETURN gds.util.asNode(nodeId).name AS name, communityId
ORDER BY communityId, name ASC
name  communityId 

"Kingston upon Thames" 
0 
"Liverpool" 
0 
"Surbiton" 
0 
"Sliven" 
1 
"Xánthi" 
1 
"Malmö" 
2 
"Solna" 
2 
"Örkelljunga" 
2 
In the example above we can see that the cities are geographically clustered together.
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.kmeans.stats('cities', {
nodeProperty: 'coordinates',
k: 3,
randomSeed: 42
})
YIELD communityDistribution
communityDistribution 

{max=3, mean=2.6666666666666665, min=2, p1=2, p10=2, p25=2, p5=2, p50=3, p75=3, p90=3, p95=3, p99=3, p999=3} 
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 cluster 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.
cities
graph:CALL gds.kmeans.mutate('cities', {
nodeProperty: 'coordinates',
k: 3,
randomSeed: 42,
mutateProperty: 'kmeans'
})
YIELD communityDistribution
communityDistribution 

{max=3, mean=2.6666666666666665, min=2, p1=2, p10=2, p25=2, p5=2, p50=3, p75=3, p90=3, p95=3, p99=3, p999=3} 
In mutate
mode, only a single row is returned by the procedure.
The result is written to the GDS inmemory graph instead of the Neo4j database.
Write
The write
execution mode extends the stats
mode with an important side effect: writing the cluster 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.kmeans.write('cities', {
nodeProperty: 'coordinates',
k: 3,
randomSeed: 42,
writeProperty: 'kmeans'
})
YIELD nodePropertiesWritten
nodePropertiesWritten 

8 
In write
mode, only a single row is returned by the procedure.
The result is written to the Neo4j database instead of the GDS inmemory graph.
Seeding initial centroids
We now see the effect that seeding centroids has on KMeans. We run KMeans with initial seeds the coordinates of New York, Amsterdam, and Rome.
CALL gds.kmeans.stream('cities', {
nodeProperty: 'coordinates',
k: 3,
seedCentroids: [[40.712776,74.005974], [52.370216,4.895168],[41.902782,12.496365]]
})
YIELD nodeId, communityId
RETURN gds.util.asNode(nodeId).name AS name, communityId
ORDER BY communityId, name ASC
name  communityId 

"Kingston upon Thames" 
1 
"Liverpool" 
1 
"Malmö" 
1 
"Solna" 
1 
"Surbiton" 
1 
"Örkelljunga" 
1 
"Sliven" 
2 
"Xánthi" 
2 
Notice that in this case the cities have been geographically clustered into two clusters: one contains cities in Northern Europe whereas the other contains in Southern Europe. On the other hand, the cluster with New York as the initial centroid was not the closest to any city at the first phase.