gives the graph join of the graphs g1 and g2.

Details and Options


open allclose all

Basic Examples  (3)

Join two graphs:

Plot the structure of the adjacency matrices:

Generate wheel graphs:

Complete graphs :

Generate dipyramid graphs:

Scope  (29)

Directed Graphs  (5)

GraphJoin works with directed graphs:

Simple directed graphs:

Directed multigraphs:

Directed weighted graphs:

Directed annotated graphs:

Undirected Graphs  (5)

GraphJoin works with undirected graphs:

Simple undirected graphs:

Undirected multigraphs:

Undirected weighted graphs:

Undirected annotated graphs:

Mixed Graphs  (5)

GraphJoin works with mixed graphs:

Simple mixed graphs:

Mixed multigraphs:

Mixed weighted graphs:

Mixed annotated graphs:

Multigraphs  (5)

GraphJoin works with multigraphs:

Directed multigraphs:

Mixed multigraphs:

Weighted multigraphs:

Annotated multigraphs:

Weighted Graphs  (5)

GraphJoin works with weighted graphs:

Directed weighted graphs:

Undirected weighted graphs:

Mixed weighted graphs:

Annotated weighted graphs:

Special Graphs  (4)

GraphJoin works on entity graphs:

GraphJoin works on trees:

Use rules to specify the graph:

GraphJoin works with more than two graphs:

Properties & Relations  (4)

Joining the adjacency matrix of two graphs on diagonal and others are ones gets the adjacency matrix of GraphJoin:

The join of a single vertex to an empty graph gets a star graph:

The join of a single vertex to a cycle graph gets a wheel graph :

The join of empty graphs on , , ... nodes gets a complete -partite graph :

Wolfram Research (2022), GraphJoin, Wolfram Language function,


Wolfram Research (2022), GraphJoin, Wolfram Language function,


Wolfram Language. 2022. "GraphJoin." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2022). GraphJoin. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_graphjoin, author="Wolfram Research", title="{GraphJoin}", year="2022", howpublished="\url{}", note=[Accessed: 14-June-2024 ]}


@online{reference.wolfram_2024_graphjoin, organization={Wolfram Research}, title={GraphJoin}, year={2022}, url={}, note=[Accessed: 14-June-2024 ]}