ButterflyGraph[n]
returns the n-dimensional butterfly graph, a directed graph whose vertices are pairs , where
is a binary string of length n and
is an integer in the range 0 through n and whose edges go from vertex
to
, if
is identical to
in all bits with the possible exception of the
bit. Here bits are counted left to right. An option VertexLabel, with default setting False, is allowed. When this option is set to True, vertices are labeled with strings
.


ButterflyGraph
ButterflyGraph[n]
returns the n-dimensional butterfly graph, a directed graph whose vertices are pairs , where
is a binary string of length n and
is an integer in the range 0 through n and whose edges go from vertex
to
, if
is identical to
in all bits with the possible exception of the
bit. Here bits are counted left to right. An option VertexLabel, with default setting False, is allowed. When this option is set to True, vertices are labeled with strings
.
Details and Options
- ButterflyGraph functionality is now available in the built-in Wolfram Language function ButterflyGraph.
- To use ButterflyGraph, you first need to load the Combinatorica Package using Needs["Combinatorica`"].
See Also
Tech Notes
Related Guides
-
▪
- Built-in Graphs ▪
- Graphs & Networks ▪
- Graph Visualization ▪
- Computation on Graphs ▪
- Graph Construction & Representation ▪
- Graphs and Matrices ▪
- Graph Properties & Measurements ▪
- Graph Operations and Modifications ▪
- Statistical Analysis ▪
- Social Network Analysis ▪
- Graph Properties ▪
- Mathematical Data Formats ▪
- Discrete Mathematics
Text
Wolfram Research (2012), ButterflyGraph, Wolfram Language function, https://reference.wolfram.com/language/Combinatorica/ref/ButterflyGraph.html.
CMS
Wolfram Language. 2012. "ButterflyGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/Combinatorica/ref/ButterflyGraph.html.
APA
Wolfram Language. (2012). ButterflyGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/Combinatorica/ref/ButterflyGraph.html
BibTeX
@misc{reference.wolfram_2025_butterflygraph, author="Wolfram Research", title="{ButterflyGraph}", year="2012", howpublished="\url{https://reference.wolfram.com/language/Combinatorica/ref/ButterflyGraph.html}", note=[Accessed: 10-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_butterflygraph, organization={Wolfram Research}, title={ButterflyGraph}, year={2012}, url={https://reference.wolfram.com/language/Combinatorica/ref/ButterflyGraph.html}, note=[Accessed: 10-August-2025]}