PathGraph
PathGraph[{v_{1},v_{2},…}]
yields a path with vertices v_{i} and edges between v_{i} and v_{i+1 }.
PathGraph[{e_{1},e_{2},…}]
yields a path with edges e_{j}.
PathGraph[{v_{1},v_{2},…},{e_{1},e_{2},…}]
yields a path with vertices v_{i} and edges e_{j}.
PathGraph[{…,w_{i}[v_{i},…],…},{…,w_{j}[e_{j},…],…}]
yields a path with vertex and edge properties defined by the symbolic wrappers w_{k}.
PathGraph[{v_{i}v_{j},…}]
uses rules v_{i}>v_{j} to specify a path.
Details and Options
 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 indegree one and at most outdegree one.
 PathGraph can only represent selfavoiding paths, except for cycles.

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 to interpret Rule as DirectedEdge 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
List of all options
Examples
open allclose allScope (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:
Options (82)
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)
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 builtin settings for EdgeShapeFunction:
Undirected edges including the basic line:
Lines with different glyphs on the edges:
Directed edges including solid 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:
GraphHighlightStyle (2)
Get a list of builtin settings for GraphHighlightStyle:
Use builtin 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)
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 any expression as a label:
Use Placed with symbolic locations to control label placement, including outside positions:
Symbolic outside corner positions:
Symbolic inside corner positions:
Use explicit coordinates to place the center of labels:
Place all labels at the upperright 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:
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 builtin collections for VertexShapeFunction:
Use builtin settings for VertexShapeFunction in the "Basic" collection:
Use builtin settings for VertexShapeFunction in the "Rounded" collection:
Use builtin settings for VertexShapeFunction in the "Concave" collection:
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)
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:
Applications (6)
The GraphCenter of path graphs:
The GraphPeriphery:
The VertexEccentricity:
Highlight the vertex eccentricity path:
The GraphRadius:
The GraphDiameter:
Visualize different centralities for PathGraph:
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 loopfree 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:
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