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EmptyGraphQ
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EmptyGraphQ

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yields True if g is an empty graph and False otherwise.

Details

  • A graph is considered empty if it has no edges.

Examples

open allclose all

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

Test whether a graph is empty:

In[1]:=1
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https://wolfram.com/xid/0b8dbi7jgj-f1e9fa
Out[1]=1

Non-empty graphs:

In[1]:=1
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https://wolfram.com/xid/0b8dbi7jgj-cgx5d
Out[1]=1

Scope  (6)Survey of the scope of standard use cases

EmptyGraphQ works with undirected graphs:

In[3]:=3
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https://wolfram.com/xid/0b8dbi7jgj-fgkyo1
Out[3]=3

Directed graphs:

In[1]:=1
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https://wolfram.com/xid/0b8dbi7jgj-gx301e
Out[1]=1

Multigraphs:

In[1]:=1
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https://wolfram.com/xid/0b8dbi7jgj-uvnf7h
Out[1]=1

Mixed graphs:

In[1]:=1
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https://wolfram.com/xid/0b8dbi7jgj-5geyu
Out[1]=1

EmptyGraphQ gives False for expressions that are not edgeless graphs:

In[1]:=1
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https://wolfram.com/xid/0b8dbi7jgj-3l2bwe
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0b8dbi7jgj-i52fbz
Out[2]=2

EmptyGraphQ works with large graphs:

In[1]:=1
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https://wolfram.com/xid/0b8dbi7jgj-q1if7j
In[2]:=2
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https://wolfram.com/xid/0b8dbi7jgj-vdyffa
Out[2]=2

Properties & Relations  (7)Properties of the function, and connections to other functions

The number of edges of an empty graph is zero:

In[3]:=3
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https://wolfram.com/xid/0b8dbi7jgj-er32m5
Out[3]=3

The vertex degree for an empty graph is all zeros:

In[1]:=1
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https://wolfram.com/xid/0b8dbi7jgj-fp066
Out[1]=1

The empty graphs are undirected graphs:

In[1]:=1
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https://wolfram.com/xid/0b8dbi7jgj-frb7q
Out[1]=1

The complement of a complete graph is an empty graph:

In[1]:=1
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https://wolfram.com/xid/0b8dbi7jgj-fzmbqy
Out[1]=1

The intersection of two graphs with different names is an empty graph:

In[1]:=1
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https://wolfram.com/xid/0b8dbi7jgj-efyy0k
Out[1]=1

The intersection of any graph and its complement is an empty graph:

In[1]:=1
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https://wolfram.com/xid/0b8dbi7jgj-es3og
In[2]:=2
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https://wolfram.com/xid/0b8dbi7jgj-b5yq85
Out[2]=2

The adjacency matrix for an empty graph has all zero entries:

In[1]:=1
✖
https://wolfram.com/xid/0b8dbi7jgj-bebck2
Wolfram Research (2010), EmptyGraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/EmptyGraphQ.html.
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Wolfram Research (2010), EmptyGraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/EmptyGraphQ.html.

Text

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

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

CMS

Wolfram Language. 2010. "EmptyGraphQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/EmptyGraphQ.html.

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Wolfram Language. 2010. "EmptyGraphQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/EmptyGraphQ.html.

APA

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

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

BibTeX

@misc{reference.wolfram_2025_emptygraphq, author="Wolfram Research", title="{EmptyGraphQ}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/EmptyGraphQ.html}", note=[Accessed: 29-March-2025 ]}

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@misc{reference.wolfram_2025_emptygraphq, author="Wolfram Research", title="{EmptyGraphQ}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/EmptyGraphQ.html}", note=[Accessed: 29-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_emptygraphq, organization={Wolfram Research}, title={EmptyGraphQ}, year={2010}, url={https://reference.wolfram.com/language/ref/EmptyGraphQ.html}, note=[Accessed: 29-March-2025 ]}

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@online{reference.wolfram_2025_emptygraphq, organization={Wolfram Research}, title={EmptyGraphQ}, year={2010}, url={https://reference.wolfram.com/language/ref/EmptyGraphQ.html}, note=[Accessed: 29-March-2025 ]}