BooleanGraph [bfunc,g1,…,gn]
gives the Boolean graph defined by the Boolean function bfunc on the graphs g1, …, gn.
BooleanGraph
BooleanGraph [bfunc,g1,…,gn]
gives the Boolean graph defined by the Boolean function bfunc on the graphs g1, …, gn.
Details and Options
- The Boolean graph has a vertex list given by the union of vertex lists.
- An edge uv is in the resulting graph if bfunc[EdgeQ [g1,uv],…,EdgeQ [gn,uv]] is True .
- An edge uv is in the resulting graph if bfunc[EdgeQ [gi,uv],…,EdgeQ [gn,uv]] is True .
- GraphUnion [g1,g2] is equivalent to BooleanGraph [Or ,g1,g2].
- GraphIntersection [g1,g2] is equivalent to BooleanGraph [And ,g1,g2].
- GraphDifference [g1,g2] is equivalent to BooleanGraph [#1∧¬#2&,g1,g2].
- BooleanGraph works with undirected graphs, directed graphs, multigraphs, and mixed graphs.
Examples
open all close allBasic Examples (1)
The Boolean combination of two graphs:
Scope (5)
BooleanGraph works with undirected graphs:
Directed graphs:
BooleanGraph works with as many graphs as the Boolean function:
Multigraphs:
Mixed graphs:
Applications (4)
Define the symmetric graph difference Xor :
Convert the Boolean expression Xor to disjunctive normal form:
Implement it by related functions:
Compare to the result by using Xor directly:
Define the graph Nand :
Convert the Boolean expression Nand to disjunctive normal form:
Implement it by related functions:
Compare to the result by using Nand directly:
Define the graph Nor :
Convert the Boolean expression Nor to disjunctive normal form:
Implement it by related functions:
Compare to the result by using Nor directly:
Compute the Boolean graph for all Boolean functions of two variables:
Use BooleanFunction to enumerate all Boolean functions of two variables:
Compute the Boolean graph using these functions:
Properties & Relations (3)
GraphUnion corresponds to Or :
GraphIntersection corresponds to And :
BooleanGraph does not necessarily produce simple graphs:
Use SimpleGraph if only a simple graph is needed:
Related Guides
Text
Wolfram Research (2010), BooleanGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/BooleanGraph.html (updated 2014).
CMS
Wolfram Language. 2010. "BooleanGraph." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/BooleanGraph.html.
APA
Wolfram Language. (2010). BooleanGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BooleanGraph.html
BibTeX
@misc{reference.wolfram_2025_booleangraph, author="Wolfram Research", title="{BooleanGraph}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/BooleanGraph.html}", note=[Accessed: 11-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_booleangraph, organization={Wolfram Research}, title={BooleanGraph}, year={2014}, url={https://reference.wolfram.com/language/ref/BooleanGraph.html}, note=[Accessed: 11-January-2026]}