DirectedGraph
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DirectedGraph
Details and Options
- A directed graph is also known as a digraph.
- DirectedGraph[g] is equivalent to DirectedGraph[g,Automatic].
- The following conversions conv can be used:
-
Automatic convert 
to both 
and 
"Acyclic" convert 
to 
if u precedes v in the vertex list and 
otherwise"Random" convert 
to either 
or 
randomly - DirectedGraph takes the same options as Graph.
- DirectedGraph works with undirected graphs, multigraphs, and mixed graphs.
-
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 allBasic Examples (3)Summary of the most common use cases
Convert each undirected edge of the graph to both directions:
In[1]:=1
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https://wolfram.com/xid/0i1ovmowq-b2a430
Out[1]=1
In[1]:=1
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https://wolfram.com/xid/0i1ovmowq-gfi1fn
Out[1]=1
A direction according to the vertex order in the vertex list:
In[1]:=1
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https://wolfram.com/xid/0i1ovmowq-e85o59
Out[1]=1
Scope (6)Survey of the scope of standard use cases
The input is unchanged for directed graphs:
In[2]:=2
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https://wolfram.com/xid/0i1ovmowq-07dy5
Out[2]=2
DirectedGraph works with undirected graphs:
In[1]:=1
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https://wolfram.com/xid/0i1ovmowq-kctn0i
Out[1]=1
In[1]:=1
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https://wolfram.com/xid/0i1ovmowq-633iry
Out[1]=1
In[1]:=1
✖
https://wolfram.com/xid/0i1ovmowq-feud0
Out[1]=1
Use rules to specify the graph:
In[1]:=1
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https://wolfram.com/xid/0i1ovmowq-bndh30
Out[1]=1
DirectedGraph works with large graphs:
In[1]:=1
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https://wolfram.com/xid/0i1ovmowq-wxgjyb
In[2]:=2
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https://wolfram.com/xid/0i1ovmowq-zavwg0
Out[2]=2
Applications (1)Sample problems that can be solved with this function
Properties & Relations (3)Properties of the function, and connections to other functions
A directed graph can be constructed by a list of DirectedEdge objects:
In[1]:=1
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https://wolfram.com/xid/0i1ovmowq-li4snf
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0i1ovmowq-dvvh45
Out[2]=2
A graph is either undirected or directed:
In[1]:=1
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https://wolfram.com/xid/0i1ovmowq-ouppi
In[2]:=2
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https://wolfram.com/xid/0i1ovmowq-o98wrl
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0i1ovmowq-ezaznq
Out[3]=3
A nonsymmetric adjacency matrix is interpreted to be a directed graph:
In[1]:=1
✖
https://wolfram.com/xid/0i1ovmowq-bhrtvw
In[2]:=2
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https://wolfram.com/xid/0i1ovmowq-ebo5iw
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0i1ovmowq-b937kg
Out[3]=3
Use DirectedEdges->False to interpret it as an undirected graph:
In[4]:=4
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https://wolfram.com/xid/0i1ovmowq-dbmka8
Out[4]=4
Wolfram Research (2010), DirectedGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/DirectedGraph.html (updated 2015).
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Wolfram Research (2010), DirectedGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/DirectedGraph.html (updated 2015).Text
Wolfram Research (2010), DirectedGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/DirectedGraph.html (updated 2015).
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Wolfram Research (2010), DirectedGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/DirectedGraph.html (updated 2015).CMS
Wolfram Language. 2010. "DirectedGraph." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/DirectedGraph.html.
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Wolfram Language. 2010. "DirectedGraph." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/DirectedGraph.html.APA
Wolfram Language. (2010). DirectedGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DirectedGraph.html
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Wolfram Language. (2010). DirectedGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DirectedGraph.htmlBibTeX
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@misc{reference.wolfram_2025_directedgraph, author="Wolfram Research", title="{DirectedGraph}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/DirectedGraph.html}", note=[Accessed: 29-May-2025
]}BibLaTeX
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@online{reference.wolfram_2025_directedgraph, organization={Wolfram Research}, title={DirectedGraph}, year={2015}, url={https://reference.wolfram.com/language/ref/DirectedGraph.html}, note=[Accessed: 29-May-2025
]}