# K-Nearest Neighbors

## 1. Introduction

The K-Nearest Neighbors algorithm computes a distance value for all node pairs in the graph and creates new relationships between each node and its k nearest neighbors. The distance is calculated based on node properties.

The input of this algorithm is a monopartite graph. The graph does not need to be connected, in fact, existing relationships between nodes will be ignored - apart from random walk sampling if that that initial sampling option is used. New relationships are created between each node and its k nearest neighbors.

The K-Nearest Neighbors algorithm compares given properties of each node. The `k` nodes where these properties are most similar are the k-nearest neighbors.

The initial set of neighbors is picked at random and verified and refined in multiple iterations. The number of iterations is limited by the configuration parameter `maxIterations`. The algorithm may stop earlier if the neighbor lists only change by a small amount, which can be controlled by the configuration parameter `deltaThreshold`.

The particular implementation is based on Efficient k-nearest neighbor graph construction for generic similarity measures by Wei Dong et al. Instead of comparing every node with every other node, the algorithm selects possible neighbors based on the assumption, that the neighbors-of-neighbors of a node are most likely already the nearest one. The algorithm scales quasi-linear with respect to the node count, instead of being quadratic.

Furthermore, the algorithm only compares a sample of all possible neighbors on each iteration, assuming that eventually all possible neighbors will be seen. This can be controlled with the configuration parameter `sampleRate`:

• A valid sample rate must be in between 0 (exclusive) and 1 (inclusive).

• The default value is `0.5`.

• The parameter is used to control the trade-off between accuracy and runtime-performance.

• A higher sample rate will increase the accuracy of the result.

• The algorithm will also require more memory and will take longer to compute.

• A lower sample rate will increase the runtime-performance.

• Some potential nodes may be missed in the comparison and may not be included in the result.

When encountered neighbors have equal similarity to the least similar already known neighbor, randomly selecting which node to keep can reduce the risk of some neighborhoods not being explored. This behavior is controlled by the configuration parameter `perturbationRate`.

The output of the algorithm are new relationships between nodes and their k-nearest neighbors. Similarity scores are expressed via relationship properties.

It is also possible to apply filtering on the source and/or target nodes in the produced similarity pairs. You can consider the filtered K-Nearest Neighbors algorithm for this purpose.

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

### 1.1. Similarity metrics

The similarity measure used in the KNN algorithm depends on the type of the configured node properties. KNN supports both scalar numeric values and lists of numbers.

#### 1.1.1. Scalar numbers

When a property is a scalar number, the similarity is computed as follows: Figure 1. one divided by one plus the absolute difference

This gives us a number in the range `(0, 1]`.

#### 1.1.2. List of integers

When a property is a list of integers, similarity can be measured with either the Jaccard similarity or the Overlap coefficient.

Jaccard similarity Figure 2. size of intersection divided by size of union
Overlap coefficient Figure 3. size of intersection divided by size of minimum set

Both of these metrics give a score in the range `[0, 1]` and no normalization needs to be performed. Jaccard similarity is used as the default option for comparing lists of integers when the metric is not specified.

#### 1.1.3. List of floating-point numbers

When a property is a list of floating-point numbers, there are three alternatives for computing similarity between two nodes.

The default metric used is that of Cosine similarity.

Cosine similarity Figure 4. dot product of the vectors divided by the product of their lengths

Notice that the above formula gives a score in the range of `[-1, 1]` . The score is normalized into the range `[0, 1]` by doing `score = (score + 1) / 2`.

The other two metrics include the Pearson correlation score and Normalized Euclidean similarity.

Pearson correlation score Figure 5. covariance divided by the product of the standard deviations

As above, the formula gives a score in the range `[-1, 1]`, which is normalized into the range `[0, 1]` similarly.

Euclidean similarity Figure 6. the root of the sum of the square difference between each pair of elements

The result from this formula is a non-negative value, but is not necessarily bounded into the `[0, 1]` range. Τo bound the number into this range and obtain a similarity score, we return `score = 1 / (1 + distance)`, i.e., we perform the same normalization as in the case of scalar values.

#### 1.1.4. Multiple properties

Finally, when multiple properties are specified, the similarity of the two neighbors is the mean of the similarities of the individual properties, i.e. the simple mean of the numbers, each of which is in the range `[0, 1]`, giving a total score also in the `[0, 1]` range.

 The validity of this mean is highly context dependent, so take care when applying it to your data domain.

#### 1.1.5. Node properties and metrics configuration

The node properties and metrics to use are specified with the `nodeProperties` configuration parameter. At least one node property must be specified.

This parameter accepts one of:

 a single property name `nodeProperties: 'embedding'` a Map of property keys to metrics ```nodeProperties: { embedding: 'COSINE', age: 'DEFAULT', lotteryNumbers: 'OVERLAP' }``` list of Strings and/or Maps ```nodeProperties: [ {embedding: 'COSINE'}, 'age', {lotteryNumbers: 'OVERLAP'} ]```

The available metrics by type are:

Table 2. Available metrics by type
type metric

List of Integer

`JACCARD`, `OVERLAP`

List of Float

`COSINE`, `EUCLIDEAN`, `PEARSON`

For any property type, `DEFAULT` can also be specified to use the default metric. For scalar numbers, there is only the default metric.

### 1.2. Initial neighbor sampling

The algorithm starts off by picking `k` random neighbors for each node. There are two options for how this random sampling can be done.

Uniform

The first `k` neighbors for each node are chosen uniformly at random from all other nodes in the graph. This is the classic way of doing the initial sampling. It is also the algorithm’s default. Note that this method does not actually use the topology of the input graph.

Random Walk

From each node we take a depth biased random walk and choose the first `k` unique nodes we visit on that walk as our initial random neighbors. If after some internally defined `O(k)` number of steps a random walk, `k` unique neighbors have not been visited, we will fill in the remaining neighbors using the uniform method described above. The random walk method makes use of the input graph’s topology and may be suitable if it is more likely to find good similarity scores between topologically close nodes.

 The random walk used is biased towards depth in the sense that it will more likely choose to go further away from its previously visited node, rather that go back to it or to a node equidistant to it. The intuition of this bias is that subsequent iterations of comparing neighbor-of-neighbors will likely cover the extended (topological) neighborhood of each node.

## 2. Syntax

This section covers the syntax used to execute the K-Nearest Neighbors 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.

K-Nearest Neighbors syntax per mode
Run K-Nearest Neighbors in stream mode on a named graph.
``````CALL gds.knn.stream(
graphName: String,
configuration: Map
) YIELD
node1: Integer,
node2: Integer,
similarity: Float``````
Table 3. 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 4. General configuration for algorithm execution on a named graph.
Name Type Default Optional Description

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 5. Algorithm specific configuration
Name Type Default Optional Description

nodeProperties

String or Map or List of Strings / Maps

`n/a`

no

The node properties to use for similarity computation along with their selected similarity metrics. Accepts a single property key, a Map of property keys to metrics, or a List of property keys and/or Maps, as above. See Node properties and metrics configuration for details.

topK

Integer

`10`

yes

The number of neighbors to find for each node. The K-nearest neighbors are returned. This value cannot be lower than 1.

sampleRate

Float

`0.5`

yes

Sample rate to limit the number of comparisons per node. Value must be between 0 (exclusive) and 1 (inclusive).

deltaThreshold

Float

`0.001`

yes

Value as a percentage to determine when to stop early. If fewer updates than the configured value happen, the algorithm stops. Value must be between 0 (exclusive) and 1 (inclusive).

maxIterations

Integer

`100`

yes

Hard limit to stop the algorithm after that many iterations.

randomJoins

Integer

`10`

yes

The number of random attempts per node to connect new node neighbors based on random selection, for each iteration.

initialSampler

String

`"uniform"`

yes

The method used to sample the first `k` random neighbors for each node. "uniform" and "randomWalk", both case-insensitive, are valid inputs.

randomSeed

Integer

`n/a`

yes

The seed value to control the randomness of the algorithm. Note that `concurrency` must be set to 1 when setting this parameter.

similarityCutoff

Float

`0`

yes

Filter out from the list of K-nearest neighbors nodes with similarity below this threshold.

perturbationRate

Float

`0`

yes

The probability of replacing the least similar known neighbor with an encountered neighbor of equal similarity.

Table 6. Results
Name Type Description

`node1`

Integer

Node ID of the first node.

`node2`

Integer

Node ID of the second node.

`similarity`

Float

Similarity score for the two nodes.

Run K-Nearest Neighbors in stats mode on a named graph.
``````CALL gds.knn.stats(
graphName: String,
configuration: Map
)
YIELD
preProcessingMillis: Integer,
computeMillis: Integer,
postProcessingMillis: Integer,
nodesCompared: Integer,
ranIterations: Integer,
didConverge: Boolean,
nodePairsConsidered: Integer,
similarityPairs: Integer,
similarityDistribution: Map,
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. General configuration for algorithm execution on a named graph.
Name Type Default Optional Description

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. Algorithm specific configuration
Name Type Default Optional Description

nodeProperties

String or Map or List of Strings / Maps

`n/a`

no

The node properties to use for similarity computation along with their selected similarity metrics. Accepts a single property key, a Map of property keys to metrics, or a List of property keys and/or Maps, as above. See Node properties and metrics configuration for details.

topK

Integer

`10`

yes

The number of neighbors to find for each node. The K-nearest neighbors are returned. This value cannot be lower than 1.

sampleRate

Float

`0.5`

yes

Sample rate to limit the number of comparisons per node. Value must be between 0 (exclusive) and 1 (inclusive).

deltaThreshold

Float

`0.001`

yes

Value as a percentage to determine when to stop early. If fewer updates than the configured value happen, the algorithm stops. Value must be between 0 (exclusive) and 1 (inclusive).

maxIterations

Integer

`100`

yes

Hard limit to stop the algorithm after that many iterations.

randomJoins

Integer

`10`

yes

The number of random attempts per node to connect new node neighbors based on random selection, for each iteration.

initialSampler

String

`"uniform"`

yes

The method used to sample the first `k` random neighbors for each node. "uniform" and "randomWalk", both case-insensitive, are valid inputs.

randomSeed

Integer

`n/a`

yes

The seed value to control the randomness of the algorithm. Note that `concurrency` must be set to 1 when setting this parameter.

similarityCutoff

Float

`0`

yes

Filter out from the list of K-nearest neighbors nodes with similarity below this threshold.

perturbationRate

Float

`0`

yes

The probability of replacing the least similar known neighbor with an encountered neighbor of equal similarity.

Table 10. Results
Name Type Description

ranIterations

Integer

Number of iterations run.

didConverge

Boolean

Indicates if the algorithm converged.

nodePairsConsidered

Integer

The number of similarity computations.

preProcessingMillis

Integer

Milliseconds for preprocessing the data.

computeMillis

Integer

Milliseconds for running the algorithm.

postProcessingMillis

Integer

Milliseconds for computing similarity value distribution statistics.

nodesCompared

Integer

The number of nodes for which similarity was computed.

similarityPairs

Integer

The number of similarities in the result.

similarityDistribution

Map

Map containing min, max, mean as well as p50, p75, p90, p95, p99 and p999 percentile values of the computed similarity results.

configuration

Map

The configuration used for running the algorithm.

Run K-Nearest Neighbors in mutate mode on a graph stored in the catalog.
``````CALL gds.knn.mutate(
graphName: String,
configuration: Map
)
YIELD
preProcessingMillis: Integer,
computeMillis: Integer,
mutateMillis: Integer,
postProcessingMillis: Integer,
relationshipsWritten: Integer,
nodesCompared: Integer,
ranIterations: Integer,
didConverge: Boolean,
nodePairsConsidered: Integer,
similarityDistribution: Map,
configuration: Map``````
Table 11. 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 12. General configuration for algorithm execution on a named graph.
Name Type Default Optional Description

mutateRelationshipType

String

`n/a`

no

The relationship type used for the new relationships written to the projected graph.

mutateProperty

String

`n/a`

no

The relationship property in the GDS graph to which the similarity score 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 13. Algorithm specific configuration
Name Type Default Optional Description

nodeProperties

String or Map or List of Strings / Maps

`n/a`

no

The node properties to use for similarity computation along with their selected similarity metrics. Accepts a single property key, a Map of property keys to metrics, or a List of property keys and/or Maps, as above. See Node properties and metrics configuration for details.

topK

Integer

`10`

yes

The number of neighbors to find for each node. The K-nearest neighbors are returned. This value cannot be lower than 1.

sampleRate

Float

`0.5`

yes

Sample rate to limit the number of comparisons per node. Value must be between 0 (exclusive) and 1 (inclusive).

deltaThreshold

Float

`0.001`

yes

Value as a percentage to determine when to stop early. If fewer updates than the configured value happen, the algorithm stops. Value must be between 0 (exclusive) and 1 (inclusive).

maxIterations

Integer

`100`

yes

Hard limit to stop the algorithm after that many iterations.

randomJoins

Integer

`10`

yes

The number of random attempts per node to connect new node neighbors based on random selection, for each iteration.

initialSampler

String

`"uniform"`

yes

The method used to sample the first `k` random neighbors for each node. "uniform" and "randomWalk", both case-insensitive, are valid inputs.

randomSeed

Integer

`n/a`

yes

The seed value to control the randomness of the algorithm. Note that `concurrency` must be set to 1 when setting this parameter.

similarityCutoff

Float

`0`

yes

Filter out from the list of K-nearest neighbors nodes with similarity below this threshold.

perturbationRate

Float

`0`

yes

The probability of replacing the least similar known neighbor with an encountered neighbor of equal similarity.

Table 14. Results
Name Type Description

ranIterations

Integer

Number of iterations run.

didConverge

Boolean

Indicates if the algorithm converged.

nodePairsConsidered

Integer

The number of similarity computations.

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 similarity value distribution statistics.

nodesCompared

Integer

The number of nodes for which similarity was computed.

relationshipsWritten

Integer

The number of relationships created.

similarityDistribution

Map

Map containing min, max, mean, stdDev and p1, p5, p10, p25, p75, p90, p95, p99, p100 percentile values of the computed similarity results.

configuration

Map

The configuration used for running the algorithm.

Run K-Nearest Neighbors in write mode on a graph stored in the catalog.
``````CALL gds.knn.write(
graphName: String,
configuration: Map
)
YIELD
preProcessingMillis: Integer,
computeMillis: Integer,
writeMillis: Integer,
postProcessingMillis: Integer,
nodesCompared: Integer,
ranIterations: Integer,
didConverge: Boolean,
nodePairsConsidered: Integer,
relationshipsWritten: Integer,
similarityDistribution: Map,
configuration: Map``````
Table 15. 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 16. General configuration for algorithm execution on a named graph.
Name Type Default Optional Description

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.

writeConcurrency

Integer

`value of 'concurrency'`

yes

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

writeRelationshipType

String

`n/a`

no

The relationship type used to persist the computed relationships in the Neo4j database.

writeProperty

String

`n/a`

no

The relationship property in the Neo4j database to which the similarity score is written.

Table 17. Algorithm specific configuration
Name Type Default Optional Description

nodeProperties

String or Map or List of Strings / Maps

`n/a`

no

The node properties to use for similarity computation along with their selected similarity metrics. Accepts a single property key, a Map of property keys to metrics, or a List of property keys and/or Maps, as above. See Node properties and metrics configuration for details.

topK

Integer

`10`

yes

The number of neighbors to find for each node. The K-nearest neighbors are returned. This value cannot be lower than 1.

sampleRate

Float

`0.5`

yes

Sample rate to limit the number of comparisons per node. Value must be between 0 (exclusive) and 1 (inclusive).

deltaThreshold

Float

`0.001`

yes

Value as a percentage to determine when to stop early. If fewer updates than the configured value happen, the algorithm stops. Value must be between 0 (exclusive) and 1 (inclusive).

maxIterations

Integer

`100`

yes

Hard limit to stop the algorithm after that many iterations.

randomJoins

Integer

`10`

yes

The number of random attempts per node to connect new node neighbors based on random selection, for each iteration.

initialSampler

String

`"uniform"`

yes

The method used to sample the first `k` random neighbors for each node. "uniform" and "randomWalk", both case-insensitive, are valid inputs.

randomSeed

Integer

`n/a`

yes

The seed value to control the randomness of the algorithm. Note that `concurrency` must be set to 1 when setting this parameter.

similarityCutoff

Float

`0`

yes

Filter out from the list of K-nearest neighbors nodes with similarity below this threshold.

perturbationRate

Float

`0`

yes

The probability of replacing the least similar known neighbor with an encountered neighbor of equal similarity.

Table 18. Results
Name Type Description

ranIterations

Integer

Number of iterations run.

didConverge

Boolean

Indicates if the algorithm converged.

nodePairsConsidered

Integer

The number of similarity computations.

preProcessingMillis

Integer

Milliseconds for preprocessing the data.

computeMillis

Integer

Milliseconds for running the algorithm.

writeMillis

Integer

Milliseconds for writing result data back to Neo4j.

postProcessingMillis

Integer

Milliseconds for computing similarity value distribution statistics.

nodesCompared

Integer

The number of nodes for which similarity was computed.

relationshipsWritten

Integer

The number of relationships created.

similarityDistribution

Map

Map containing min, max, mean, stdDev and p1, p5, p10, p25, p75, p90, p95, p99, p100 percentile values of the computed similarity results.

configuration

Map

The configuration used for running the algorithm.

 The KNN algorithm does not read any relationships, but the values for `relationshipProjection` or `relationshipQuery` are still being used and respected for the graph loading.

The results are the same as running write mode on a named graph, see write mode syntax above.

 To get a deterministic result when running the algorithm: the `concurrency` parameter must be set to one the `randomSeed` must be explicitly set.

## 3. Examples

In this section we will show examples of running the KNN algorithm on a concrete graph. With the Uniform sampler, KNN samples initial neighbors uniformly at random, and doesn’t take into account graph topology. This means KNN can run on a graph of only nodes, without any relationships. Consider the following graph of five disconnected Person nodes. ``````CREATE (alice:Person {name: 'Alice', age: 24, lotteryNumbers: [1, 3], embedding: [1.0, 3.0]})
CREATE (bob:Person {name: 'Bob', age: 73, lotteryNumbers: [1, 2, 3], embedding: [2.1, 1.6]})
CREATE (carol:Person {name: 'Carol', age: 24, lotteryNumbers: , embedding: [1.5, 3.1]})
CREATE (dave:Person {name: 'Dave', age: 48, lotteryNumbers: [2, 4], embedding: [0.6, 0.2]})
CREATE (eve:Person {name: 'Eve', age: 67, lotteryNumbers: [1, 5], embedding: [1.8, 2.7]});``````

In the example, we want to use the K-Nearest Neighbors algorithm to compare people based on either their age or a combination on all provided properties.

 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: {
properties: ['age','lotteryNumbers','embedding']
}
},
'*'
);``````

### 3.1. 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.

The following will estimate the memory requirements for running the algorithm:
``````CALL gds.knn.write.estimate('myGraph', {
nodeProperties: ['age'],
writeRelationshipType: 'SIMILAR',
writeProperty: 'score',
topK: 1
})
YIELD nodeCount, bytesMin, bytesMax, requiredMemory``````
Table 19. Results
nodeCount bytesMin bytesMax requiredMemory

5

2096

3152

"[2096 Bytes ... 3152 Bytes]"

### 3.2. Stream

In the `stream` execution mode, the algorithm returns the similarity score for each relationship. 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, and stream results:
``````CALL gds.knn.stream('myGraph', {
topK: 1,
nodeProperties: ['age'],
// The following parameters are set to produce a deterministic result
randomSeed: 1337,
concurrency: 1,
sampleRate: 1.0,
deltaThreshold: 0.0
})
YIELD node1, node2, similarity
RETURN gds.util.asNode(node1).name AS Person1, gds.util.asNode(node2).name AS Person2, similarity
ORDER BY similarity DESCENDING, Person1, Person2``````
Table 20. Results
Person1 Person2 similarity

"Alice"

"Carol"

1.0

"Carol"

"Alice"

1.0

"Bob"

"Eve"

0.14285714285714285

"Eve"

"Bob"

0.14285714285714285

"Dave"

"Eve"

0.05

We use default values for the procedure configuration parameter for most parameters. The `randomSeed` and `concurrency` is set to produce the same result on every invocation. The `topK` parameter is set to 1 to only return the single nearest neighbor for every node. Notice that the similarity between Dave and Eve is very low. Setting the `similarityCutoff` parameter to 0.10 will filter the relationship between them, removing it from the result.

### 3.3. 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.

The following will run the algorithm and return the result in form of statistical and measurement values:
``````CALL gds.knn.stats('myGraph', {topK: 1, concurrency: 1, randomSeed: 42, nodeProperties: ['age']})
YIELD nodesCompared, similarityPairs``````
Table 21. Results
nodesCompared similarityPairs

5

5

### 3.4. Mutate

The `mutate` execution mode extends the `stats` mode with an important side effect: updating the named graph with a new relationship property containing the similarity score for that relationship. 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.

The following will run the algorithm, and write back results to the in-memory graph:
``````CALL gds.knn.mutate('myGraph', {
mutateRelationshipType: 'SIMILAR',
mutateProperty: 'score',
topK: 1,
randomSeed: 42,
concurrency: 1,
nodeProperties: ['age']
})
YIELD nodesCompared, relationshipsWritten``````
Table 22. Results
nodesCompared relationshipsWritten

5

5

As we can see from the results, the number of created relationships is equal to the number of rows in the streaming example.

 The relationships that are produced by the mutation are always directed, even if the input graph is undirected. If for example `a → b` is topK for `a` and symmetrically `b → a` is topK for `b`, it appears as though an undirected relationship is produced. However, they are just two directed relationships that have been independently produced.

### 3.5. Write

The `write` execution mode extends the `stats` mode with an important side effect: for each pair of nodes we create a relationship with the similarity score as a property to the Neo4j database. The type of the new relationship is specified using the mandatory configuration parameter `writeRelationshipType`. Each new relationship stores the similarity score between the two nodes it represents. The relationship property key is set using the mandatory configuration parameter `writeProperty`. The result is a single summary row, similar to `stats`, but with some additional metrics.

For more details on the `write` mode in general, see Write.

The following will run the algorithm, and write back results:
``````CALL gds.knn.write('myGraph', {
writeRelationshipType: 'SIMILAR',
writeProperty: 'score',
topK: 1,
randomSeed: 42,
concurrency: 1,
nodeProperties: ['age']
})
YIELD nodesCompared, relationshipsWritten``````
Table 23. Results
nodesCompared relationshipsWritten

5

5

As we can see from the results, the number of created relationships is equal to the number of rows in the streaming example.

 The relationships that are written are always directed, even if the input graph is undirected. If for example `a → b` is topK for `a` and symmetrically `b → a` is topK for `b`, it appears as though an undirected relationship is written. However, they are just two directed relationships that have been independently written.

### 3.6. Calculation with multiple properties

If we want to calculate similarity based on multiple metrics, we can calculate the similarity for each property individually and take their mean. As an example, we can use the Normalized Euclidean similarity metric for the embedding property and the Overlap metric for the lottery numbers property in addition to the age property.

The following shows an example of using multiple properties to calculate similarity and streams the results:
``````CALL gds.knn.stream('myGraph', {
topK: 1,
nodeProperties: [
{embedding: "EUCLIDEAN"},
'age',
{lotteryNumbers: "OVERLAP"}
],
// The following parameters are set to produce a deterministic result
randomSeed: 1337,
concurrency: 1,
sampleRate: 1.0,
deltaThreshold: 0.0
})
YIELD node1, node2, similarity
RETURN gds.util.asNode(node1).name AS Person1, gds.util.asNode(node2).name AS Person2, similarity
ORDER BY similarity DESCENDING, Person1, Person2``````
Table 24. Results
Person1 Person2 similarity

"Alice"

"Carol"

0.931216931216931

"Carol"

"Alice"

0.931216931216931

"Bob"

"Carol"

0.432336103416436

"Eve"

"Alice"

0.366920651602733

"Dave"

"Bob"

0.243466706038683

Note that the two distinct maps in the query could be merged to a single one.