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: 28-October-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: 28-October-2025]}