This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# PathGraph

 PathGraph yields a path with vertices and edges between and . PathGraphyields a path with edges . PathGraphyields a path with vertices and edges . PathGraphyields a path with vertex and edge properties defined by the symbolic wrappers .
• 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.
A path constructed from a list of vertices:
A list of edges:
A path constructed from a list of vertices:
 Out[1]=
 Out[2]=

A list of edges:
 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:
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:
Highlight the vertex eccentricity path:
Highlight the diameter path:
Visualize different centralities for PathGraph:
Highlight the closeness centrality:
Highlight the eigenvector centrality:
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 :
New in 8