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PathGraph [{v1,v2,}]

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

PathGraph [{e1,e2,}]

yields a path with edges ej.

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

yields a path with vertices vi and edges ej.

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

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

PathGraph [{vivj,}]

uses rules vi->vj to specify a path.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Connectivity  
Options  
AnnotationRules  
DirectedEdges  
EdgeLabels  
Show More Show More
EdgeShapeFunction  
EdgeStyle  
EdgeWeight  
GraphHighlight  
GraphHighlightStyle  
GraphLayout  
PlotTheme  
Base Themes  
Feature Themes  
VertexCoordinates  
VertexLabels  
VertexShape  
VertexShapeFunction  
VertexSize  
VertexStyle  
VertexWeight  
Applications  
Properties & Relations  
See Also
Related Guides
History
Cite this Page

PathGraph [{v1,v2,}]

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

PathGraph [{e1,e2,}]

yields a path with edges ej.

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

yields a path with vertices vi and edges ej.

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

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

PathGraph [{vivj,}]

uses rules vi->vj to specify a path.

Details and Options

Examples

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Basic Examples  (2)

A path constructed from a list of vertices:

A list of edges:

Scope  (6)

Connectivity  (6)

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

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

Create a directed graph from a list of rules:

Create an undirected graph from a list of rules:

Use VertexList and EdgeList to get vertices and edges:

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

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

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

The input vertex list controls the resulting vertex order:

Any expression can be used as vertices:

Options  (82)

AnnotationRules  (3)

Specify an annotation for vertices:

Edges:

Graph itself:

DirectedEdges  (2)

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

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

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

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 using Placed in a wrapper:

Any number of labels can be used:

Place multiple labels using EdgeLabels :

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 using Placed in a wrapper:

Any number of labels can be used:

Place multiple labels using VertexLabels :

Use the argument to 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 can be combined with 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 a 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  (6)

The GraphCenter of path graphs:

The GraphPeriphery :

The VertexEccentricity :

Highlight the vertex eccentricity path:

The GraphRadius :

Highlight the radius path:

The GraphDiameter :

Highlight the diameter path:

Visualize different centralities for PathGraph :

Highlight the closeness centrality:

Highlight the eigenvector centrality:

Properties & Relations  (10)

Use VertexCount and EdgeCount to count vertices and edges:

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

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

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

Compute the IncidenceMatrix from a graph:

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

A path graph is a loop-free graph:

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

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

A path graph with no repeated vertices is a tree:

A path graph with no repeated vertices is acyclic:

The line graph of a path is isomorphic to :

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).

CMS

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

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: 05-December-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: 05-December-2025]}

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