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MultigraphQ[g]

yields True if the graph g is a multigraph and False otherwise.

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Basic Examples  
Scope  
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MultigraphQ

MultigraphQ[g]

yields True if the graph g is a multigraph and False otherwise.

Details

  • A graph is a multigraph if there are multiple undirected edges or multiple directed edges with the same direction between the same vertices.

Examples

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Basic Examples  (2)

Test whether a graph has multiple edges:

Wolfram Language code: Graph[{12, 23, 31, 31}]
Wolfram Language code: MultigraphQ[%]

MultigraphQ gives False for inputs that are not graphs with multiple edges:

Wolfram Language code: CompleteGraph[4]
Wolfram Language code: MultigraphQ[%]

Scope  (2)

MultigraphQ gives False for expressions that are not graphs:

Wolfram Language code: MultigraphQ[x]

MultigraphQ works with large graphs:

Wolfram Language code: m = SparseArray[{Band[{1, 2}] -> 1, {1, 3} -> 2, Band[{1, 4}] -> 1}, {100000, 100000}];
Wolfram Language code: g = AdjacencyGraph[m];
Wolfram Language code: MultigraphQ[g]//Timing

Properties & Relations  (2)

A PathGraph has no multiple edges:

Wolfram Language code: PathGraph[{12, 23}]
Wolfram Language code: {PathGraphQ[%], MultigraphQ[%]}

The adjacency matrix of a graph with multiple edges has some entries greater than 1:

Wolfram Language code: g = {Graph[{12, 12, 23, 31}], Graph[{12, 12, 23, 31}]}
Wolfram Language code: MultigraphQ /@ g
Wolfram Language code: MatrixForm /@ AdjacencyMatrix /@ g

Its incidence matrix has repeated columns:

Wolfram Language code: MatrixForm /@ IncidenceMatrix /@ g

Possible Issues  (1)

MultigraphQ gives False for non-explicit graphs:

Wolfram Language code: MultigraphQ[CompleteGraph[n]]
Wolfram Research (2014), MultigraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/MultigraphQ.html.

Text

Wolfram Research (2014), MultigraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/MultigraphQ.html.

CMS

Wolfram Language. 2014. "MultigraphQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MultigraphQ.html.

APA

Wolfram Language. (2014). MultigraphQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MultigraphQ.html

BibTeX

@misc{reference.wolfram_2026_multigraphq, author="Wolfram Research", title="{MultigraphQ}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/MultigraphQ.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_multigraphq, organization={Wolfram Research}, title={MultigraphQ}, year={2014}, url={https://reference.wolfram.com/language/ref/MultigraphQ.html}, note=[Accessed: 12-June-2026]}