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GraphTriangleCount
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GraphTriangleCount

New in 14.1

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gives the number of triangles in the graph g.

Details

Examples

open allclose all

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

Count triangles in a graph:

In[1]:=1
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https://wolfram.com/xid/0dc169ub65ci-co2cc7
In[2]:=2
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https://wolfram.com/xid/0dc169ub65ci-gd1l6
Out[2]=2

Count triangles in social networks:

In[1]:=1
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https://wolfram.com/xid/0dc169ub65ci-v42p3x
In[2]:=2
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https://wolfram.com/xid/0dc169ub65ci-81jtpt
Out[2]=2

Scope  (4)Survey of the scope of standard use cases

GraphTriangleCount works with undirected graphs:

In[1]:=1
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https://wolfram.com/xid/0dc169ub65ci-b1cxtq
Out[1]=1

Directed graphs:

In[1]:=1
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https://wolfram.com/xid/0dc169ub65ci-cy689y
Out[1]=1

Use rules to specify the graph:

In[1]:=1
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https://wolfram.com/xid/0dc169ub65ci-bndh30
Out[1]=1

GraphTriangleCount works with large graphs:

In[1]:=1
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https://wolfram.com/xid/0dc169ub65ci-lkg873
In[2]:=2
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https://wolfram.com/xid/0dc169ub65ci-gfgajd
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0dc169ub65ci-b5ef0w
Out[3]=3

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

Compute the transitivity of a graph:

In[1]:=1
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https://wolfram.com/xid/0dc169ub65ci-jwozp4
In[4]:=4
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https://wolfram.com/xid/0dc169ub65ci-qwcclh
Out[4]=4

Compare with GlobalClusteringCoefficient:

In[5]:=5
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https://wolfram.com/xid/0dc169ub65ci-c2jxkn
Out[5]=5

Properties & Relations  (2)Properties of the function, and connections to other functions

Use MatrixPower to count triangles in a graph:

In[15]:=15
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https://wolfram.com/xid/0dc169ub65ci-rpqfjz
In[16]:=16
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https://wolfram.com/xid/0dc169ub65ci-3tc3r
Out[16]=16
In[18]:=18
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https://wolfram.com/xid/0dc169ub65ci-v32ac
Out[18]=18

Use FindCycle to list triangles in a graph:

In[1]:=1
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https://wolfram.com/xid/0dc169ub65ci-w4bz9o
In[2]:=2
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https://wolfram.com/xid/0dc169ub65ci-292kd0
In[3]:=3
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https://wolfram.com/xid/0dc169ub65ci-7xuvse
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0dc169ub65ci-tsjraj
Out[4]=4

Possible Issues  (1)Common pitfalls and unexpected behavior

Multi-edges are ignored:

In[1]:=1
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https://wolfram.com/xid/0dc169ub65ci-ekcu4f
Out[1]=1
Wolfram Research (2024), GraphTriangleCount, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphTriangleCount.html.
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Wolfram Research (2024), GraphTriangleCount, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphTriangleCount.html.

Text

Wolfram Research (2024), GraphTriangleCount, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphTriangleCount.html.

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Wolfram Research (2024), GraphTriangleCount, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphTriangleCount.html.

CMS

Wolfram Language. 2024. "GraphTriangleCount." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GraphTriangleCount.html.

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Wolfram Language. 2024. "GraphTriangleCount." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GraphTriangleCount.html.

APA

Wolfram Language. (2024). GraphTriangleCount. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GraphTriangleCount.html

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Wolfram Language. (2024). GraphTriangleCount. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GraphTriangleCount.html

BibTeX

@misc{reference.wolfram_2025_graphtrianglecount, author="Wolfram Research", title="{GraphTriangleCount}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/GraphTriangleCount.html}", note=[Accessed: 08-July-2025 ]}

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@misc{reference.wolfram_2025_graphtrianglecount, author="Wolfram Research", title="{GraphTriangleCount}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/GraphTriangleCount.html}", note=[Accessed: 08-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_graphtrianglecount, organization={Wolfram Research}, title={GraphTriangleCount}, year={2024}, url={https://reference.wolfram.com/language/ref/GraphTriangleCount.html}, note=[Accessed: 08-July-2025 ]}

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@online{reference.wolfram_2025_graphtrianglecount, organization={Wolfram Research}, title={GraphTriangleCount}, year={2024}, url={https://reference.wolfram.com/language/ref/GraphTriangleCount.html}, note=[Accessed: 08-July-2025 ]}