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UndirectedGraph[g]

gives an undirected graph from the directed graph g.

UndirectedGraph[{vw,…}]

uses rules vw to specify the graph g.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Properties & Relations  
See Also
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UndirectedGraph

UndirectedGraph[g]

gives an undirected graph from the directed graph g.

UndirectedGraph[{vw,…}]

uses rules vw to specify the graph g.

Details and Options

  • The undirected edge uv is an edge in the resulting undirected graph if either of the directed edges uv or vu is an edge of g.
  • UndirectedGraph works with directed graphs, multigraphs, and mixed graphs.

Examples

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Basic Examples  (1)

Give an undirected graph from a directed graph:

Wolfram Language code: UndirectedGraph[[image]]

Scope  (7)

The input is unchanged for undirected graphs:

Wolfram Language code: UndirectedGraph[[image]]

UndirectedGraph works with directed graphs:

Wolfram Language code: UndirectedGraph[[image]]

Multigraphs:

Wolfram Language code: UndirectedGraph[[image]]

Mixed graphs:

Wolfram Language code: UndirectedGraph[[image]]

Use rules to specify the graph:

Wolfram Language code: UndirectedGraph[{1 -> 3, 2 -> 1, 3 -> 6, 4 -> 6, 1 -> 5, 5 -> 4, 6 -> 1}]

Directed edges with different directions convert to one undirected edge:

Wolfram Language code: UndirectedGraph[[image]]

UndirectedGraph works with large graphs:

Wolfram Language code: g = AdjacencyGraph[SparseArray[{{i_, i_} -> 1, {i_, j_} /; j == i + 1 -> 1}, {10 ^ 6, 10 ^ 6}]];
Wolfram Language code: Timing[h = UndirectedGraph[g];]
Wolfram Language code: UndirectedGraphQ /@ {g, h}
Wolfram Language code: EdgeCount /@ {g, h}

Properties & Relations  (4)

An undirected graph can be constructed by a list of UndirectedEdge objects:

Wolfram Language code: Graph[{UndirectedEdge[1, 2], UndirectedEdge[2, 3], UndirectedEdge[3, 1]}]
Wolfram Language code: UndirectedGraphQ[%]

A graph is either undirected or directed:

Wolfram Language code: g1 = [image];g2 = [image];
Wolfram Language code: UndirectedGraphQ /@ {g1, g2}
Wolfram Language code: DirectedGraphQ /@ {g1, g2}

A symmetric adjacency matrix is interpreted to be an undirected graph:

Wolfram Language code: (m = {{0, 1, 1}, {1, 0, 1}, {1, 1, 0}})//MatrixForm
Wolfram Language code: SymmetricMatrixQ[m]
Wolfram Language code: UndirectedGraphQ[AdjacencyGraph[m]]

Use DirectedEdges->True to interpret it as a directed graph:

Wolfram Language code: UndirectedGraphQ[AdjacencyGraph[m, DirectedEdges -> True]]

The incidence matrix of an undirected graph has no negative entries:

Wolfram Language code: g = Graph[{12, 23, 31}]
Wolfram Language code: UndirectedGraphQ[g]
Wolfram Language code: IncidenceMatrix[g]//MatrixForm
Wolfram Research (2010), UndirectedGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/UndirectedGraph.html (updated 2015).

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_undirectedgraph, author="Wolfram Research", title="{UndirectedGraph}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/UndirectedGraph.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_undirectedgraph, organization={Wolfram Research}, title={UndirectedGraph}, year={2015}, url={https://reference.wolfram.com/language/ref/UndirectedGraph.html}, note=[Accessed: 13-June-2026]}