# Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# NearestNeighborGraph

NearestNeighborGraph[{elem1,elem2,}]
gives a graph with vertices elem1,elem2, and edges connecting each elemi to its nearest neighbors.

NearestNeighborGraph[{elem1,elem2,},k]
gives a graph connecting each elemi to its k nearest neighbors.

NearestNeighborGraph[{elem1,elem2,},{k,r}]
gives a graph connecting each elemi to at most k nearest vertices within radius r of elemi.

NearestNeighborGraph[{elem1,elem2,},{All,r}]
gives a graph connecting each elemi to all vertices within radius r of elemi.

## Details and OptionsDetails and Options

• The nearest neighbor graph is also known as k-nearest neighbor graph (k-NNG).
• An element elemj is a nearest neighbor of an element elemi whenever the distance from elemi to elemj is no larger than the distance from elemi to any other element.
• An element elemj is a k-nearest neighbor of an element elemi whenever the distance from elemi to elemj is among the k smallest distances from elemi to any other element.
• NearestNeighborGraph works for a variety of data, including numerical, geospatial, textual, and visual.
• NearestNeighborGraph has the same options as Graph, with the following additions and changes:
•  DirectedEdges Automatic whether edges should be taken to be directed DistanceFunction Automatic the distance metric or dissimilarity to use WorkingPrecision Automatic precision to use for numeric data
• NearestNeighborGraph takes the same DistanceFunction as Nearest.

## ExamplesExamplesopen allclose all

### Basic Examples  (2)Basic Examples  (2)

A nearest neighbor graph:

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Generate the k-nearest neighbor graph for integers in the range 1 to 10:

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