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FindGraphIsomorphism
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FindGraphIsomorphism

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finds an isomorphism that maps the graph g1 to g2 by renaming vertices.

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finds at most n isomorphisms.

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FindGraphIsomorphism[{vw,…},…]

uses rules vw to specify the graph g.

Details and Options

Examples

open allclose all

Basic Examples  (2)Summary of the most common use cases

Find an isomorphism that maps two graphs:

In[1]:=1
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https://wolfram.com/xid/0rkgdpvtjbdtg14-f5edt
Out[1]=1

Find all isomorphisms:

In[1]:=1
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https://wolfram.com/xid/0rkgdpvtjbdtg14-guputi
Out[1]=1

Scope  (8)Survey of the scope of standard use cases

Specification  (5)

FindGraphIsomorphism works with undirected graphs:

In[1]:=1
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https://wolfram.com/xid/0rkgdpvtjbdtg14-d9n8ou
Out[1]=1

Directed graphs:

In[1]:=1
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https://wolfram.com/xid/0rkgdpvtjbdtg14-bjwckj
Out[1]=1

Use rules to specify the graph:

In[1]:=1
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https://wolfram.com/xid/0rkgdpvtjbdtg14-bndh30
Out[1]=1

It returns an empty list if no isomorphism can be found:

In[1]:=1
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https://wolfram.com/xid/0rkgdpvtjbdtg14-b83ts
Out[1]=1

FindGraphIsomorphism works with large graphs:

In[1]:=1
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https://wolfram.com/xid/0rkgdpvtjbdtg14-fl62op
In[2]:=2
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https://wolfram.com/xid/0rkgdpvtjbdtg14-hx93y
In[3]:=3
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https://wolfram.com/xid/0rkgdpvtjbdtg14-4iugm
Out[3]=3

Enumeration  (3)

Find an isomorphism that maps two graphs:

In[1]:=1
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https://wolfram.com/xid/0rkgdpvtjbdtg14-cvsbaj
Out[1]=1

Find at most two isomorphisms:

In[1]:=1
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https://wolfram.com/xid/0rkgdpvtjbdtg14-j7b3rh
Out[1]=1

Find all isomorphisms:

In[1]:=1
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https://wolfram.com/xid/0rkgdpvtjbdtg14-kewkuy
Out[1]=1

Applications  (1)Sample problems that can be solved with this function

Find an isomorphism that maps two graphs:

In[1]:=1
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https://wolfram.com/xid/0rkgdpvtjbdtg14-cmg60p
In[2]:=2
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https://wolfram.com/xid/0rkgdpvtjbdtg14-hyregk
In[3]:=3
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https://wolfram.com/xid/0rkgdpvtjbdtg14-cvr7dg
In[4]:=4
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https://wolfram.com/xid/0rkgdpvtjbdtg14-nagfe
In[5]:=5
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https://wolfram.com/xid/0rkgdpvtjbdtg14-da11ma
Out[5]=5

Highlight and label two graphs according to the mapping:

In[6]:=6
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https://wolfram.com/xid/0rkgdpvtjbdtg14-bc8hxs
In[7]:=7
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https://wolfram.com/xid/0rkgdpvtjbdtg14-frhw52
In[8]:=8
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https://wolfram.com/xid/0rkgdpvtjbdtg14-g2k4x2
Out[8]=8

Properties & Relations  (3)Properties of the function, and connections to other functions

Isomorphic graphs have the same number of vertices and edges:

In[1]:=1
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https://wolfram.com/xid/0rkgdpvtjbdtg14-baigi
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0rkgdpvtjbdtg14-c1suyl
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0rkgdpvtjbdtg14-subr3
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0rkgdpvtjbdtg14-ch2vsv
Out[4]=4

Test whether two graphs are isomorphic using IsomorphicGraphQ:

In[1]:=1
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https://wolfram.com/xid/0rkgdpvtjbdtg14-f4vgcx
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0rkgdpvtjbdtg14-fw1rxe
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0rkgdpvtjbdtg14-b8ah4f
Out[3]=3

Isomorphic graphs have the same canonical graph:

In[1]:=1
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https://wolfram.com/xid/0rkgdpvtjbdtg14-gawxbw
In[2]:=2
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https://wolfram.com/xid/0rkgdpvtjbdtg14-bzde4x
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0rkgdpvtjbdtg14-bbygwo
Out[3]=3
Wolfram Research (2010), FindGraphIsomorphism, Wolfram Language function, https://reference.wolfram.com/language/ref/FindGraphIsomorphism.html (updated 2015).
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Wolfram Research (2010), FindGraphIsomorphism, Wolfram Language function, https://reference.wolfram.com/language/ref/FindGraphIsomorphism.html (updated 2015).

Text

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

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

CMS

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

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

APA

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

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

BibTeX

@misc{reference.wolfram_2025_findgraphisomorphism, author="Wolfram Research", title="{FindGraphIsomorphism}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FindGraphIsomorphism.html}", note=[Accessed: 19-June-2025 ]}

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@misc{reference.wolfram_2025_findgraphisomorphism, author="Wolfram Research", title="{FindGraphIsomorphism}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FindGraphIsomorphism.html}", note=[Accessed: 19-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_findgraphisomorphism, organization={Wolfram Research}, title={FindGraphIsomorphism}, year={2015}, url={https://reference.wolfram.com/language/ref/FindGraphIsomorphism.html}, note=[Accessed: 19-June-2025 ]}

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@online{reference.wolfram_2025_findgraphisomorphism, organization={Wolfram Research}, title={FindGraphIsomorphism}, year={2015}, url={https://reference.wolfram.com/language/ref/FindGraphIsomorphism.html}, note=[Accessed: 19-June-2025 ]}