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IndexGraph[g]

replaces the vertices of the graph g by its vertex indices.

IndexGraph[g,r]

replaces the vertices with integers r, r+1, ….

IndexGraph[{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
Related Guides
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IndexGraph

IndexGraph[g]

replaces the vertices of the graph g by its vertex indices.

IndexGraph[g,r]

replaces the vertices with integers r, r+1, ….

IndexGraph[{vw,…},…]

uses rules vw to specify the graph g.

Details and Options

  • IndexGraph works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

Examples

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Basic Examples  (2)

Replace the vertices of the graph with their vertex indices:

Wolfram Language code: IndexGraph[[image]]

Replace the vertices with indices starting from 6:

Wolfram Language code: IndexGraph[[image], 6]

Scope  (7)

IndexGraph works with undirected graphs:

Wolfram Language code: IndexGraph[[image], 10]

Directed graphs:

Wolfram Language code: IndexGraph[[image], 10]

Multigraphs:

Wolfram Language code: IndexGraph[[image], 10]

Mixed graphs:

Wolfram Language code: IndexGraph[[image], 10]

Replace the vertices with negative indices:

Wolfram Language code: IndexGraph[[image], -10]

Use rules to specify the graph:

Wolfram Language code: IndexGraph[{1 -> 3, 2 -> 1, 3 -> 6, 4 -> 6, 1 -> 5, 5 -> 4, 6 -> 1}, 10]

IndexGraph works with large graphs:

Wolfram Language code: g = GridGraph[{10, 10, 10, 10}];
Wolfram Language code: Timing[h = IndexGraph[g, VertexCount[g] + 1];]
Wolfram Language code: {VertexCount[h], EdgeCount[h]}

Properties & Relations  (5)

IndexGraph has the same number of vertices as the original graph:

Wolfram Language code: g = [image];
Wolfram Language code: VertexCount[g] == VertexCount[IndexGraph[g, 10]]

IndexGraph has the same number of edges as the original graph:

Wolfram Language code: g = [image];
Wolfram Language code: EdgeCount[g] == EdgeCount[IndexGraph[g, 10]]

IndexGraph is isomorphic to the original graph:

Wolfram Language code: g = [image];
Wolfram Language code: IsomorphicGraphQ[g, IndexGraph[g, 20]]

Use VertexReplace to replace the vertices of the graph:

Wolfram Language code: {VertexReplace[[image], {1 -> 5, 2 -> 6, 3 -> 7, 4 -> 8}], IndexGraph[[image], 5]}

IndexGraph has the same adjacency matrix as the original graph:

Wolfram Language code: g = RandomGraph[{10, 20}]
Wolfram Language code: MatrixPlot[AdjacencyMatrix[#]]& /@ {g, IndexGraph[g, 20]}
Wolfram Research (2010), IndexGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/IndexGraph.html (updated 2015).

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_indexgraph, author="Wolfram Research", title="{IndexGraph}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/IndexGraph.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_indexgraph, organization={Wolfram Research}, title={IndexGraph}, year={2015}, url={https://reference.wolfram.com/language/ref/IndexGraph.html}, note=[Accessed: 13-June-2026]}