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EmptyGraphQ[g]

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

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EmptyGraphQ

EmptyGraphQ[g]

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

Details

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

Examples

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Basic Examples  (2)

Test whether a graph is empty:

Wolfram Language code: EmptyGraphQ[Graph[{1, 2}, {}]]

Non-empty graphs:

Wolfram Language code: EmptyGraphQ[[image]]

Scope  (6)

EmptyGraphQ works with undirected graphs:

Wolfram Language code: EmptyGraphQ[[image]]

Directed graphs:

Wolfram Language code: EmptyGraphQ[[image]]

Multigraphs:

Wolfram Language code: EmptyGraphQ[[image]]

Mixed graphs:

Wolfram Language code: EmptyGraphQ[[image]]

EmptyGraphQ gives False for expressions that are not edgeless graphs:

Wolfram Language code: EmptyGraphQ[x]
Wolfram Language code: EmptyGraphQ[Graph[garbage]]

EmptyGraphQ works with large graphs:

Wolfram Language code: GridGraph[{10, 10, 10, 10}];
Wolfram Language code: EmptyGraphQ[%]//Timing

Properties & Relations  (8)

The number of edges of an empty graph is zero:

Wolfram Language code: {EmptyGraphQ[[image]], EdgeCount[[image]]}

The vertex degree for an empty graph is all zeros:

Wolfram Language code: {EmptyGraphQ[[image]], VertexDegree[[image]]}

The null graph is empty, has zero edges and vertices and has no vertex degrees:

Wolfram Language code: Through[{EmptyGraphQ, VertexCount, EdgeCount, VertexDegree}[Graph[{}]]]

The empty graphs are undirected graphs:

Wolfram Language code: {UndirectedGraphQ[[image]], DirectedGraphQ[[image]]}

The complement of a complete graph is an empty graph:

Wolfram Language code: EmptyGraphQ[GraphComplement[[image]]]

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

Wolfram Language code: EmptyGraphQ[GraphIntersection[[image], [image]]]

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

Wolfram Language code: g = [image];
Wolfram Language code: EmptyGraphQ[GraphIntersection[g, GraphComplement[g]]]

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

Wolfram Language code: AdjacencyMatrix[[image]]//MatrixForm
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.

CMS

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

BibTeX

@misc{reference.wolfram_2026_emptygraphq, author="Wolfram Research", title="{EmptyGraphQ}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/EmptyGraphQ.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_emptygraphq, organization={Wolfram Research}, title={EmptyGraphQ}, year={2010}, url={https://reference.wolfram.com/language/ref/EmptyGraphQ.html}, note=[Accessed: 13-June-2026]}