WOLFRAM

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PathGraph[{v1,v2,}]

yields a path with vertices vi and edges between vi and vi+1 .

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PathGraph[{e1,e2,}]

yields a path with edges ej.

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PathGraph[{v1,v2,},{e1,e2,}]

yields a path with vertices vi and edges ej.

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PathGraph[{,wi[vi,],},{,wj[ej,],}]

yields a path with vertex and edge properties defined by the symbolic wrappers wk.

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PathGraph[{vivj,}]

uses rules vi->vj to specify a path.

Details and Options

Examples

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Basic Examples  (2)Summary of the most common use cases

A path constructed from a list of vertices:

Out[1]=1
Out[2]=2

A list of edges:

Out[1]=1

Scope  (6)Survey of the scope of standard use cases

Connectivity  (6)

Create an undirected graph using characters, entering the character as ue:

Out[1]=1

Create a directed graph using characters, entering the character as de:

Out[1]=1

Create a directed graph from a list of rules:

Out[1]=1

Create an undirected graph from a list of rules:

Out[2]=2

Use VertexList and EdgeList to get vertices and edges:

Out[1]=1

The ordering for edges is the order in which they were entered:

Out[2]=2

The ordering for vertices is the order in which they entered in the edges:

Out[3]=3

Use an explicit vertex list to control the ordering used by VertexList:

Out[1]=1

The input vertex list controls the resulting vertex order:

Out[2]=2

Any expression can be used as vertices:

Out[1]=1
Out[2]=2

Options  (82)Common values & functionality for each option

AnnotationRules  (3)

Specify an annotation for vertices:

Out[1]=1

Edges:

Out[1]=1

Graph itself:

Out[1]=1
Out[2]=2

DirectedEdges  (2)

By default, a directed path is generated when giving a list of rules:

Out[1]=1

Use DirectedEdges->False to interpret rules as undirected edges:

Out[2]=2

Use DirectedEdge or UndirectedEdge to directly specify whether a graph is directed or not:

Out[1]=1

EdgeLabels  (7)

Label the edge 12:

Out[1]=1

Label all edges individually:

Out[2]=2

Use any expression as a label:

Out[1]=1

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

Out[1]=1

Use explicit coordinates to place labels:

Out[1]=1

Vary positions within the label:

Out[2]=2

Place multiple labels using Placed in a wrapper:

Out[1]=1

Any number of labels can be used:

Out[2]=2

Place multiple labels using EdgeLabels:

Out[3]=3

Use automatic labeling by values through Tooltip and StatusArea:

Out[1]=1
Out[2]=2

EdgeShapeFunction  (6)

Get a list of built-in settings for EdgeShapeFunction:

Out[1]=1

Undirected edges including the basic line:

Out[1]=1

Lines with different glyphs on the edges:

Out[2]=2

Directed edges including solid arrows:

Out[1]=1

Line arrows:

Out[2]=2

Open arrows:

Out[3]=3

Specify an edge function for an individual edge:

Out[1]=1

Combine with a different default edge function:

Out[2]=2

Draw edges by running a program:

Out[2]=2

EdgeShapeFunction can be combined with EdgeStyle:

Out[1]=1

EdgeShapeFunction has higher priority than EdgeStyle:

Out[2]=2

EdgeStyle  (2)

Style all edges:

Out[1]=1

Style individual edges:

Out[1]=1

EdgeWeight  (2)

Specify a weight for all edges:

Out[1]=1

Use any numeric expression as a weight:

Out[1]=1

GraphHighlight  (3)

Highlight the vertex 1:

Out[1]=1

Highlight the edge 23:

Out[1]=1

Highlight vertices and edges:

Out[1]=1

GraphHighlightStyle  (2)

Get a list of built-in settings for GraphHighlightStyle:

Out[1]=1

Use built-in settings for GraphHighlightStyle:

Out[1]=1

GraphLayout  (5)

By default, the layout is chosen automatically:

Out[1]=1

Specify layouts on special curves:

Out[1]=1

Specify layouts that satisfy optimality criteria:

Out[1]=1

VertexCoordinates overrides GraphLayout coordinates:

Out[1]=1

Use AbsoluteOptions to extract VertexCoordinates computed using a layout algorithm:

Out[1]=1
Out[2]=2

PlotTheme  (4)

Base Themes  (2)

Use a common base theme:

Out[1]=1

Use a monochrome theme:

Out[1]=1

Feature Themes  (2)

Use a large graph theme:

Out[1]=1

Use a classic diagram theme:

Out[1]=1

VertexCoordinates  (3)

By default, any vertex coordinates are computed automatically:

Out[1]=1

Extract the resulting vertex coordinates using AbsoluteOptions:

Out[2]=2

Specify a layout function along an ellipse:

Out[2]=2

Use it to generate vertex coordinates for a graph:

Out[3]=3

VertexCoordinates has higher priority than GraphLayout:

Out[1]=1

VertexLabels  (13)

Use vertex names as labels:

Out[1]=1

Label individual vertices:

Out[1]=1

Label all vertices:

Out[1]=1

Use any expression as a label:

Out[1]=1

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

Out[1]=1

Symbolic outside corner positions:

Out[2]=2

Symbolic inside positions:

Out[1]=1

Symbolic inside corner positions:

Out[2]=2

Use explicit coordinates to place the center of labels:

Out[1]=1

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

Out[1]=1

Place multiple labels using Placed in a wrapper:

Out[1]=1

Any number of labels can be used:

Out[2]=2

Place multiple labels using VertexLabels:

Out[3]=3

Use the argument to Placed to control formatting including Tooltip:

Out[1]=1

Or StatusArea:

Out[2]=2

Use more elaborate formatting functions:

Out[2]=2
Out[4]=4
Out[6]=6

VertexShape  (5)

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

Out[1]=1

Specify vertex shapes for individual vertices:

Out[1]=1

VertexShape can be combined with VertexSize:

Out[1]=1

VertexShape is not affected by VertexStyle:

Out[1]=1

VertexShapeFunction has higher priority than VertexShape:

Out[1]=1

VertexShapeFunction  (10)

Get a list of built-in collections for VertexShapeFunction:

Out[1]=1

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

Out[1]=1

Simple basic shapes:

Out[2]=2

Common basic shapes:

Out[3]=3

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

Out[1]=1
Out[2]=2

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

Out[1]=1
Out[2]=2

Draw individual vertices:

Out[1]=1

Combine with a default vertex function:

Out[2]=2

Draw vertices using a predefined graphic:

Out[1]=1

Draw vertices by running a program:

Out[2]=2

VertexShapeFunction can be combined with VertexStyle:

Out[2]=2

VertexShapeFunction has higher priority than VertexStyle:

Out[4]=4

VertexShapeFunction can be combined with VertexSize:

Out[1]=1

VertexShapeFunction has higher priority than VertexShape:

Out[1]=1

VertexSize  (8)

By default, the size of vertices is computed automatically:

Out[1]=1

Specify the size of all vertices using symbolic vertex size:

Out[1]=1

Use a fraction of the minimum distance between vertex coordinates:

Out[1]=1

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

Out[1]=1

Specify size in both the and directions:

Out[1]=1

Specify a size for individual vertices:

Out[1]=1

VertexSize can be combined with VertexShapeFunction:

Out[1]=1

VertexSize can be combined with VertexShape:

Out[1]=1

VertexStyle  (5)

Style all vertices:

Out[1]=1

Style individual vertices:

Out[1]=1

VertexShapeFunction can be combined with VertexStyle:

Out[2]=2

VertexShapeFunction has higher priority than VertexStyle:

Out[4]=4

VertexStyle can be combined with BaseStyle:

Out[1]=1

VertexStyle has higher priority than BaseStyle:

Out[2]=2

VertexShape is not affected by VertexStyle:

Out[1]=1

VertexWeight  (2)

Set the weight for all vertices:

Out[1]=1
Out[2]=2

Use any numeric expression as a weight:

Out[1]=1
Out[2]=2

Applications  (6)Sample problems that can be solved with this function

The GraphCenter of path graphs:

Out[1]=1

The GraphPeriphery:

Out[1]=1

The VertexEccentricity:

Out[1]=1

Highlight the vertex eccentricity path:

Out[3]=3

The GraphRadius:

Out[1]=1

Highlight the radius path:

Out[3]=3

The GraphDiameter:

Out[1]=1

Highlight the diameter path:

Out[3]=3

Visualize different centralities for PathGraph:

Out[3]=3

Highlight the closeness centrality:

Out[4]=4

Highlight the eigenvector centrality:

Out[5]=5

Properties & Relations  (10)Properties of the function, and connections to other functions

Use VertexCount and EdgeCount to count vertices and edges:

Out[1]=1
Out[2]=2

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

Out[2]=2

Edges and vertices are given in the order they are input:

Out[4]=4
Out[6]=6

Rows and columns of the adjacency matrix follow the order given by VertexList:

Out[2]=2

Compute the IncidenceMatrix from a graph:

The row ordering is given by VertexList and column ordering is given by EdgeList:

Out[3]=3

A path graph is a loop-free graph:

Out[1]=1
Out[2]=2

A path graph that starts and ends in the same vertex is a cycle graph:

Out[1]=1
Out[2]=2

A path graph is connected and each vertex has at most degree 2:

Out[1]=1
Out[2]=2
Out[3]=3

A path graph with no repeated vertices is a tree:

Out[1]=1

A path graph with no repeated vertices is acyclic:

Out[1]=1
Out[2]=2

The line graph of a path is isomorphic to :

Out[1]=1
Out[2]=2
Out[3]=3
Wolfram Research (2010), PathGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/PathGraph.html (updated 2015).
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Wolfram Research (2010), PathGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/PathGraph.html (updated 2015).

Text

Wolfram Research (2010), PathGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/PathGraph.html (updated 2015).

Copy to clipboard.
Wolfram Research (2010), PathGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/PathGraph.html (updated 2015).

CMS

Wolfram Language. 2010. "PathGraph." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/PathGraph.html.

Copy to clipboard.
Wolfram Language. 2010. "PathGraph." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/PathGraph.html.

APA

Wolfram Language. (2010). PathGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PathGraph.html

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Wolfram Language. (2010). PathGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PathGraph.html

BibTeX

@misc{reference.wolfram_2025_pathgraph, author="Wolfram Research", title="{PathGraph}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/PathGraph.html}", note=[Accessed: 29-March-2025 ]}

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@misc{reference.wolfram_2025_pathgraph, author="Wolfram Research", title="{PathGraph}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/PathGraph.html}", note=[Accessed: 29-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_pathgraph, organization={Wolfram Research}, title={PathGraph}, year={2015}, url={https://reference.wolfram.com/language/ref/PathGraph.html}, note=[Accessed: 29-March-2025 ]}

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@online{reference.wolfram_2025_pathgraph, organization={Wolfram Research}, title={PathGraph}, year={2015}, url={https://reference.wolfram.com/language/ref/PathGraph.html}, note=[Accessed: 29-March-2025 ]}