BUILT-IN MATHEMATICA SYMBOL

PathGraph

yields a path with vertices

and edges between

and

.

PathGraph

yields a path with edges

.

PathGraph

yields a path with vertices

and edges

.

PathGraph

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

.

MORE INFORMATION

PathGraph generates a Graph object.

PathGraph supports the same vertices, edges, wrappers, and options as Graph.

An undirected path graph is a connected graph where each vertex has at most degree two.

A directed path graph is a connected graph where each vertex has at most in-degree one and at most out-degree one.

PathGraph can only represent self-avoiding paths, except for cycles.

EXAMPLES

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Basic Examples (2)

A path constructed from a list of vertices:

A list of edges:

A path constructed from a list of vertices:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

A list of edges:

In[1]:=

Out[1]=

Scope (6)

Create an undirected graph using

characters, entering the character as Esc ue Esc:

Create a directed graph using

characters, entering the character as Esc de Esc:

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 (80)

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:

Label the edge

:

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:

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:

Style all edges:

Style individual edges:

Specify a weight for all edges:

Use any numeric expression as a weight:

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:

Highlight the vertex

:

Highlight the edge

:

Highlight vertices and edges:

Get a list of built-in settings for GraphHighlightStyle:

Use built-in settings for GraphHighlightStyle:

Get a list of built-in settings for GraphStyle:

Use built-in settings for GraphStyle:

Specify a property for vertices:

Edges:

Graph itself:

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:

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:

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:

Get a list of built-in collections for VertexShapeFunction:

Use built-in settings for VertexShapeFunction in the

collection:

Simple basic shapes:

Common basic shapes:

Use built-in settings for VertexShapeFunction in the

collection:

Use built-in settings for VertexShapeFunction in the

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:

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:

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:

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

: