# 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 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: [List of all options]
•  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.
• ## List of all options

•  AlignmentPoint Center the default point in the graphic to align with AnnotationRules {} annotations for graph, edges and vertices AspectRatio Automatic ratio of height to width Axes False whether to draw axes AxesLabel None axes labels AxesOrigin Automatic where axes should cross AxesStyle {} style specifications for the axes Background None background color for the plot BaselinePosition Automatic how to align with a surrounding text baseline BaseStyle {} base style specifications for the graphic ContentSelectable Automatic whether to allow contents to be selected CoordinatesToolOptions Automatic detailed behavior of the coordinates tool DirectedEdges Automatic whether edges should be taken to be directed DistanceFunction Automatic the distance metric or dissimilarity to use EdgeLabels None labels and label placements for edges EdgeLabelStyle Automatic style to use for edge labels EdgeShapeFunction Automatic generate graphic shapes for edges EdgeStyle Automatic style used for edges EdgeWeight Automatic weights for edges Epilog {} primitives rendered after the main plot FormatType TraditionalForm the default format type for text Frame False whether to put a frame around the plot FrameLabel None frame labels FrameStyle {} style specifications for the frame FrameTicks Automatic frame ticks FrameTicksStyle {} style specifications for frame ticks GraphHighlight {} graph elements to highlight GraphHighlightStyle Automatic style for highlight GraphLayout Automatic how to lay out vertices and edges GridLines None grid lines to draw GridLinesStyle {} style specifications for grid lines ImageMargins 0. the margins to leave around the graphic ImagePadding All what extra padding to allow for labels etc. ImageSize Automatic the absolute size at which to render the graphic LabelStyle {} style specifications for labels Method Automatic details of graphics methods to use PerformanceGoal Automatic aspects of performance to try to optimize PlotLabel None an overall label for the plot PlotRange All range of values to include PlotRangeClipping False whether to clip at the plot range PlotRangePadding Automatic how much to pad the range of values PlotRegion Automatic the final display region to be filled PlotTheme \$PlotTheme overall theme for the graph PreserveImageOptions Automatic whether to preserve image options when displaying new versions of the same graphic Prolog {} primitives rendered before the main plot RotateLabel True whether to rotate y labels on the frame Ticks Automatic axes ticks TicksStyle {} style specifications for axes ticks VertexCoordinates Automatic coordinates for vertices VertexLabels None labels and placements for vertices VertexLabelStyle Automatic style to use for vertex labels VertexShape Automatic graphic shape for vertices VertexShapeFunction Automatic generate graphic shapes for vertices VertexSize Medium size of vertices VertexStyle Automatic styles for vertices VertexWeight Automatic weights for vertices WorkingPrecision Automatic precision to use for numeric data

# Examples

open allclose all

## Basic Examples(2)

A nearest neighbor graph:

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

## Scope(10)

### Basic Uses(4)

A nearest neighbor graph for integers in the range 1 to 10:

Generate the 2-nearest neighbor graph:

Generate the at most 3-nearest neighbor graph within radius 2:

Generate the nearest neighbor graph within radius 3:

### Numerical Data(1)

A nearest neighbor graph for two-dimensional numerical data:

Three-dimensional dataset:

### Boolean Data(1)

A nearest neighbor graph for a set of Boolean data:

### Geo Positions(1)

Generate the nearest geodesic distance neighbor graph:

### Strings(1)

Generate the 2-nearest strings neighbor graph:

### Images(1)

Generate the 2-nearest images neighbor graph:

### Colors(1)

Generate the 2-nearest colors neighbor graph:

## Options(89)

### DistanceFunction(7)

By default, EuclideanDistance is used for numerical data:

EditDistance is used for strings:

GeoDistance is used for geo positions:

JaccardDissimilarity is used for Boolean data:

ColorDistance is used for colors:

ImageDistance is used for images:

The DistanceFunction can be given as a symbol:

Or as a pure function:

### Method(1)

Compare different methods for machine-precision data:

In three dimensions, the "KDtree" method is faster:

In 20 dimensions, a simple scan is faster:

### WorkingPrecision(1)

Using ensures the fastest evaluation method is used:

### AnnotationRules(2)

Specify an annotation for vertices:

Edges:

### DirectedEdges(1)

By default, an undirected graph is generated:

Use to generate a directed graph:

### EdgeLabels(7)

Label the edge 12:

Label all edges individually:

Use any expression as a label:

Use Placed with symbolic locations to control label placement along an edge:

Use explicit coordinates to place labels:

Vary positions within the label:

Place multiple labels:

Use automatic labeling by values through Tooltip and StatusArea:

### EdgeShapeFunction(6)

Get a list of built-in settings for EdgeShapeFunction:

Undirected edges including the basic line:

Lines with different glyphs on the edges:

Directed edges including solid arrows:

Line arrows:

Open arrows:

Specify an edge function for an individual edge:

Combine with a different default edge function:

Draw edges by running a program:

EdgeShapeFunction can be combined with EdgeStyle:

EdgeShapeFunction has higher priority than EdgeStyle:

### EdgeStyle(2)

Style all edges:

Style individual edges:

### EdgeWeight(2)

Specify a weight for all edges:

Use any numeric expression as a weight:

### GraphHighlight(3)

Highlight the vertex 1:

Highlight the edge 23:

Highlight vertices and edges:

### GraphHighlightStyle(2)

Get a list of built-in settings for GraphHighlightStyle:

Use built-in settings for GraphHighlightStyle:

### GraphLayout(5)

By default, the layout is chosen automatically:

Specify layouts on special curves:

Specify layouts that satisfy optimality criteria:

VertexCoordinates overrides GraphLayout coordinates:

Use AbsoluteOptions to extract VertexCoordinates computed using a layout algorithm:

### PlotTheme(4)

#### Base Themes(2)

Use a common base theme:

Use a monochrome theme:

#### Feature Themes(2)

Use a large graph theme:

Use a classic diagram theme:

### VertexCoordinates(3)

By default, any vertex coordinates are computed automatically:

Extract the resulting vertex coordinates using AbsoluteOptions:

Specify a layout function along an ellipse:

Use it to generate vertex coordinates for a graph:

VertexCoordinates has higher priority than GraphLayout:

### VertexLabels(13)

Use vertex names as labels:

Label individual vertices:

Label all vertices:

Use any expression as a label:

Use Placed with symbolic locations to control label placement, including outside positions:

Symbolic outside corner positions:

Symbolic inside positions:

Symbolic inside corner positions:

Use explicit coordinates to place the center of labels:

Place all labels at the upper-right corner of the vertex and vary the coordinates within the label:

Place multiple labels:

Any number of labels can be used:

Use the argument Placed to control formatting including Tooltip:

Or StatusArea:

Use more elaborate formatting functions:

### VertexShape(5)

Use any Graphics, Image, or Graphics3D as a vertex shape:

Specify vertex shapes for individual vertices:

VertexShape can be combined with VertexSize:

VertexShape is not affected by VertexStyle:

VertexShapeFunction has higher priority than VertexShape:

### VertexShapeFunction(10)

Get a list of built-in collections for VertexShapeFunction:

Use built-in settings for VertexShapeFunction in the "Basic" collection:

Simple basic shapes:

Common basic shapes:

Use built-in settings for VertexShapeFunction in the "Rounded" collection:

Use built-in settings for VertexShapeFunction in the "Concave" collection:

Draw individual vertices:

Combine with a default vertex function:

Draw vertices using a predefined graphic:

Draw vertices by running a program:

VertexShapeFunction can be combined with VertexStyle:

VertexShapeFunction has higher priority than VertexStyle:

VertexShapeFunction has higher priority than VertexSize:

VertexShapeFunction has higher priority than VertexShape:

### VertexSize(8)

By default, the size of vertices is computed automatically:

Specify the size of all vertices using symbolic vertex size:

Use a fraction of the minimum distance between vertex coordinates:

Use a fraction of the overall diagonal for all vertex coordinates:

Specify size in both the and directions:

Specify the size for individual vertices:

VertexSize can be combined with VertexShapeFunction:

VertexSize can be combined with VertexShape:

### VertexStyle(5)

Style all vertices:

Style individual vertices:

VertexShapeFunction can be combined with VertexStyle:

VertexShapeFunction has higher priority than VertexStyle:

VertexStyle can be combined with BaseStyle:

VertexStyle has higher priority than BaseStyle:

VertexShape is not affected by VertexStyle:

### VertexWeight(2)

Set the weight for all vertices:

Use any numeric expression as a weight:

## Applications(7)

### Basic Uses(2)

-approximate nearest neighbor search:

### Graphs & Networks(2)

Farthest neighbor graphs:

Generate a spatial random graph within radius 0.2:

### Geometry(1)

Simplification of point-sample surfaces:

### Proximity Searching(2)

Search nearest image neighbors:

Search the dictionary neighbors:

## Properties & Relations(7)

Use VertexCount and EdgeCount to count vertices and edges:

Use VertexList and EdgeList to enumerate vertices and edges in standard order:

Compute the AdjacencyMatrix from a graph:

Distance metric generates undirected graphs:

Dissimilarity generates directed graphs:

Generate a nearest neighbor graph within radius 0.2 by using SpatialGraphDistribution:

Use Nearest and NearestFunction get the nearest neighbor graph:

This is equivalent to:

Wolfram Research (2015), NearestNeighborGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/NearestNeighborGraph.html.

#### Text

Wolfram Research (2015), NearestNeighborGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/NearestNeighborGraph.html.

#### CMS

Wolfram Language. 2015. "NearestNeighborGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NearestNeighborGraph.html.

#### APA

Wolfram Language. (2015). NearestNeighborGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NearestNeighborGraph.html

#### BibTeX

@misc{reference.wolfram_2024_nearestneighborgraph, author="Wolfram Research", title="{NearestNeighborGraph}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/NearestNeighborGraph.html}", note=[Accessed: 25-April-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_nearestneighborgraph, organization={Wolfram Research}, title={NearestNeighborGraph}, year={2015}, url={https://reference.wolfram.com/language/ref/NearestNeighborGraph.html}, note=[Accessed: 25-April-2024 ]}