# GraphIntersection

GraphIntersection[g1,g2]

gives the graph intersection of the graphs g1 and g2.

GraphIntersection[g1,g2,]

gives the graph intersection of g1, g2, .

GraphIntersection[{vw,},]

uses rules vw to specify the graph g.

# Details and Options

• The graph intersection Graph[v1,e1]Graph[v2,e2] is given by Graph[v1v2,e1e2].
• GraphIntersection works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

# Examples

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## Basic Examples(1)

Obtain the graph intersection of two graphs:

Highlight the graph intersection:

## Scope(5)

GraphIntersection works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

## Properties & Relations(8)

The vertices of the graph intersection are the union of the vertices of the graphs:

The edges of the graph intersection are the intersection of the edges of the graphs:

The graph intersection of any graph and itself is isomorphic to the original graph:

The graph intersection of a graph and its subgraph has the same edges as its subgraph:

The intersection of any graph and its complement is an empty graph:

The intersection of two graphs with different names is an empty graph:

The GraphIntersection of two graphs has the same vertices as GraphUnion:

The GraphIntersection of two graphs has the same vertices as GraphDifference:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_graphintersection, author="Wolfram Research", title="{GraphIntersection}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/GraphIntersection.html}", note=[Accessed: 06-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_graphintersection, organization={Wolfram Research}, title={GraphIntersection}, year={2015}, url={https://reference.wolfram.com/language/ref/GraphIntersection.html}, note=[Accessed: 06-August-2024 ]}