TransitiveClosureGraph
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TransitiveClosureGraph
Details and Options
- TransitiveClosureGraph is also known as reachability graph.
- TransitiveClosureGraph[g] gives a graph with the same vertices as in g, and a vertex u is connected to a vertex v if there is a path from u to v in g.
- TransitiveClosureGraph takes the same options as Graph.
- Possible settings for the Method option include "Warshall", "Warren", and "Purdom". The default setting of Automatic switches among these methods depending on the graph given.
- TransitiveClosureGraph works with undirected graphs, directed graphs, and multigraphs.
-
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 (1)Summary of the most common use cases
Scope (5)Survey of the scope of standard use cases
TransitiveClosureGraph works with undirected graphs:
In[1]:=1
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https://wolfram.com/xid/0cf151i1c219cpm-bi0qon
Out[1]=1
In[1]:=1
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https://wolfram.com/xid/0cf151i1c219cpm-byonmj
Out[1]=1
In[1]:=1
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https://wolfram.com/xid/0cf151i1c219cpm-ffb0ew
Out[1]=1
Use rules to specify the graph:
In[1]:=1
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https://wolfram.com/xid/0cf151i1c219cpm-bndh30
Out[1]=1
TransitiveClosureGraph works with large graphs:
In[1]:=1
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https://wolfram.com/xid/0cf151i1c219cpm-jcp42
In[2]:=2
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https://wolfram.com/xid/0cf151i1c219cpm-bv7xtp
Out[2]=2
Options (3)Common values & functionality for each option
Method (3)
The method is automatically chosen depending on input:
In[1]:=1
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https://wolfram.com/xid/0cf151i1c219cpm-daemby
Out[1]=1
"Warshall" and "Warren" methods can be used for dense graphs:
In[1]:=1
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https://wolfram.com/xid/0cf151i1c219cpm-ts6r11
In[2]:=2
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https://wolfram.com/xid/0cf151i1c219cpm-1shz0c
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0cf151i1c219cpm-ev00ln
Out[3]=3
"Purdom" can be used for directed acyclic graphs:
In[1]:=1
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https://wolfram.com/xid/0cf151i1c219cpm-byq1n2
In[2]:=2
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https://wolfram.com/xid/0cf151i1c219cpm-bj7zu0
Out[2]=2
Applications (2)Sample problems that can be solved with this function
Find species in the food chain that would be affected if beetles were extinct:
In[1]:=1
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https://wolfram.com/xid/0cf151i1c219cpm-trr9z7
Out[1]=1
In[10]:=10
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https://wolfram.com/xid/0cf151i1c219cpm-gg1o2t
Out[10]=10
Give a divisibility tree and find all divisors for each number:
In[1]:=1
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https://wolfram.com/xid/0cf151i1c219cpm-raq66l
In[2]:=2
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https://wolfram.com/xid/0cf151i1c219cpm-fmc8i9
Out[2]=2
Properties & Relations (6)Properties of the function, and connections to other functions
The transitive closure graph has the same vertices as the original graph:
In[1]:=1
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https://wolfram.com/xid/0cf151i1c219cpm-rcxfm
In[2]:=2
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https://wolfram.com/xid/0cf151i1c219cpm-g6lw8a
Out[2]=2
An edge uv is in the closure graph if there is a path from u to v in the original graph:
In[1]:=1
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https://wolfram.com/xid/0cf151i1c219cpm-p9b3tk
There is a path from 1 to 6 in the given graph, by no direct edge:
In[2]:=2
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https://wolfram.com/xid/0cf151i1c219cpm-mgljd8
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0cf151i1c219cpm-bwze2t
Out[3]=3
There is a direct edge 16 in the transitive closure:
In[4]:=4
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https://wolfram.com/xid/0cf151i1c219cpm-bvqmlz
Out[4]=4
The transitive closure of a connected undirected graph is a complete graph:
In[1]:=1
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https://wolfram.com/xid/0cf151i1c219cpm-flcyhx
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0cf151i1c219cpm-b851o
Out[2]=2
Using transitive closure to find the reachability of each vertex in the graph:
In[1]:=1
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https://wolfram.com/xid/0cf151i1c219cpm-glg5ex
In[2]:=2
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https://wolfram.com/xid/0cf151i1c219cpm-i25ft3
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0cf151i1c219cpm-gyrql
Out[3]=3
TransitiveClosureGraph can be computed using GraphPower:
In[1]:=1
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https://wolfram.com/xid/0cf151i1c219cpm-fiqxru
In[2]:=2
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https://wolfram.com/xid/0cf151i1c219cpm-h323ua
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0cf151i1c219cpm-i5zstb
Out[3]=3
The transitive closure is the same for a graph and its transitive reduction:
In[1]:=1
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https://wolfram.com/xid/0cf151i1c219cpm-fcuv0x
In[2]:=2
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https://wolfram.com/xid/0cf151i1c219cpm-cu841o
Out[2]=2
Wolfram Research (2014), TransitiveClosureGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/TransitiveClosureGraph.html (updated 2015).
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Wolfram Research (2014), TransitiveClosureGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/TransitiveClosureGraph.html (updated 2015).Text
Wolfram Research (2014), TransitiveClosureGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/TransitiveClosureGraph.html (updated 2015).
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Wolfram Research (2014), TransitiveClosureGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/TransitiveClosureGraph.html (updated 2015).CMS
Wolfram Language. 2014. "TransitiveClosureGraph." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/TransitiveClosureGraph.html.
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Wolfram Language. 2014. "TransitiveClosureGraph." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/TransitiveClosureGraph.html.APA
Wolfram Language. (2014). TransitiveClosureGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TransitiveClosureGraph.html
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Wolfram Language. (2014). TransitiveClosureGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TransitiveClosureGraph.htmlBibTeX
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@misc{reference.wolfram_2025_transitiveclosuregraph, author="Wolfram Research", title="{TransitiveClosureGraph}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/TransitiveClosureGraph.html}", note=[Accessed: 02-April-2025
]}BibLaTeX
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@online{reference.wolfram_2025_transitiveclosuregraph, organization={Wolfram Research}, title={TransitiveClosureGraph}, year={2015}, url={https://reference.wolfram.com/language/ref/TransitiveClosureGraph.html}, note=[Accessed: 02-April-2025
]}