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UndirectedGraph
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UndirectedGraph

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gives an undirected graph from the directed graph g.

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UndirectedGraph[{vw,…}]

uses rules vw to specify the graph g.

Details and Options

  • The undirected edge uv is an edge in the resulting undirected graph if either of the directed edges uv or vu is an edge of g.
  • UndirectedGraph works with directed graphs, multigraphs, and mixed graphs.

Examples

open allclose all

Basic Examples  (1)Summary of the most common use cases

Give an undirected graph from a directed graph:

In[1]:=1
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https://wolfram.com/xid/0btoq6uup5x2-g4rnyx
Out[1]=1

Scope  (7)Survey of the scope of standard use cases

The input is unchanged for undirected graphs:

In[1]:=1
✖
https://wolfram.com/xid/0btoq6uup5x2-ll3qid
Out[1]=1

UndirectedGraph works with directed graphs:

In[1]:=1
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https://wolfram.com/xid/0btoq6uup5x2-edm5o
Out[1]=1

Multigraphs:

In[1]:=1
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https://wolfram.com/xid/0btoq6uup5x2-2v2f3n
Out[1]=1

Mixed graphs:

In[1]:=1
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https://wolfram.com/xid/0btoq6uup5x2-rlhrjj
Out[1]=1

Use rules to specify the graph:

In[1]:=1
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https://wolfram.com/xid/0btoq6uup5x2-bndh30
Out[1]=1

Directed edges with different directions convert to one undirected edge:

In[1]:=1
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https://wolfram.com/xid/0btoq6uup5x2-vi85h
Out[1]=1

UndirectedGraph works with large graphs:

In[1]:=1
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https://wolfram.com/xid/0btoq6uup5x2-n9fcxi
In[2]:=2
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https://wolfram.com/xid/0btoq6uup5x2-nf5nx4
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0btoq6uup5x2-gn2bvu
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0btoq6uup5x2-h2w1yd
Out[4]=4

Properties & Relations  (4)Properties of the function, and connections to other functions

An undirected graph can be constructed by a list of UndirectedEdge objects:

In[1]:=1
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https://wolfram.com/xid/0btoq6uup5x2-li4snf
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0btoq6uup5x2-dvvh45
Out[2]=2

A graph is either undirected or directed:

In[1]:=1
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https://wolfram.com/xid/0btoq6uup5x2-ouppi
In[2]:=2
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https://wolfram.com/xid/0btoq6uup5x2-o98wrl
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0btoq6uup5x2-ezaznq
Out[3]=3

A symmetric adjacency matrix is interpreted to be an undirected graph:

In[1]:=1
✖
https://wolfram.com/xid/0btoq6uup5x2-bhrtvw
In[2]:=2
✖
https://wolfram.com/xid/0btoq6uup5x2-ebo5iw
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0btoq6uup5x2-b937kg
Out[3]=3

Use DirectedEdges->True to interpret it as a directed graph:

In[4]:=4
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https://wolfram.com/xid/0btoq6uup5x2-dbmka8
Out[4]=4

The incidence matrix of an undirected graph has no negative entries:

In[1]:=1
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https://wolfram.com/xid/0btoq6uup5x2-d0mxjw
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0btoq6uup5x2-e45b43
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0btoq6uup5x2-c9l902
Wolfram Research (2010), UndirectedGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/UndirectedGraph.html (updated 2015).
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Wolfram Research (2010), UndirectedGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/UndirectedGraph.html (updated 2015).

Text

Wolfram Research (2010), UndirectedGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/UndirectedGraph.html (updated 2015).

✖
Wolfram Research (2010), UndirectedGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/UndirectedGraph.html (updated 2015).

CMS

Wolfram Language. 2010. "UndirectedGraph." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/UndirectedGraph.html.

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Wolfram Language. 2010. "UndirectedGraph." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/UndirectedGraph.html.

APA

Wolfram Language. (2010). UndirectedGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/UndirectedGraph.html

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Wolfram Language. (2010). UndirectedGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/UndirectedGraph.html

BibTeX

@misc{reference.wolfram_2025_undirectedgraph, author="Wolfram Research", title="{UndirectedGraph}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/UndirectedGraph.html}", note=[Accessed: 26-March-2025 ]}

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@misc{reference.wolfram_2025_undirectedgraph, author="Wolfram Research", title="{UndirectedGraph}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/UndirectedGraph.html}", note=[Accessed: 26-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_undirectedgraph, organization={Wolfram Research}, title={UndirectedGraph}, year={2015}, url={https://reference.wolfram.com/language/ref/UndirectedGraph.html}, note=[Accessed: 26-March-2025 ]}

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@online{reference.wolfram_2025_undirectedgraph, organization={Wolfram Research}, title={UndirectedGraph}, year={2015}, url={https://reference.wolfram.com/language/ref/UndirectedGraph.html}, note=[Accessed: 26-March-2025 ]}