# graphisomorphism

(To be removed) Find isomorphism between two graphs

`graphisomorphism` will be removed in a future release. Use `isomorphism` instead.

## Syntax

```[Isomorphic, Map] = graphisomorphism(G1, G2) [Isomorphic, Map] = graphisomorphism(G1, G2,'Directed', DirectedValue) ```

## Arguments

 `G1` N-by-N adjacency matrix that represents a directed or undirected graph. Nonzero entries in matrix `G1` indicate the presence of an edge. `G2` N-by-N adjacency matrix that represents a directed or undirected graph. `G2` must be the same (directed or undirected) as `G1`. `DirectedValue` Property that indicates whether the graphs are directed or undirected. Enter `false` when both `G1` and `G2` are undirected graphs. In this case, the upper triangles of the matrices `G1` and `G2` are ignored. Default is `true`, meaning that both graphs are directed.

## Description

Tip

For introductory information on graph theory functions, see Graph Theory Functions.

```[Isomorphic, Map] = graphisomorphism(G1, G2)``` returns logical 1 (`true`) in `Isomorphic` if `G1` and `G2` are isomorphic graphs, and logical 0 (`false`) otherwise. A graph isomorphism is a 1-to-1 mapping of the nodes in the graph `G1` and the nodes in the graph `G2` such that adjacencies are preserved. `G1` and `G2` are both N-by-N adjacency matrices that represent directed or undirected graphs. Return value `Isomorphic` is Boolean. When `Isomorphic` is `true`, `Map` is a row vector containing the node indices that map from `G2` to `G1` for one possible isomorphism. When `Isomorphic` is `false`, `Map` is empty. The worst-case time complexity is `O(N!)`, where `N` is the number of nodes.

```[Isomorphic, Map] = graphisomorphism(G1, G2,'Directed', DirectedValue)``` indicates whether the graphs are directed or undirected. Set `DirectedValue` to `false` when both `G1` and `G2` are undirected graphs. In this case, the upper triangles of the matrices `G1` and `G2` are ignored. Default is `true`, meaning that both graphs are directed.

## References

 Fortin, S. (1996). The Graph Isomorphism Problem. Technical Report, 96-20, Dept. of Computer Science, University of Alberta, Edomonton, Alberta, Canada.

 McKay, B.D. (1981). Practical Graph Isomorphism. Congressus Numerantium 30, 45-87.

 Siek, J.G., Lee, L-Q, and Lumsdaine, A. (2002). The Boost Graph Library User Guide and Reference Manual, (Upper Saddle River, NJ:Pearson Education).

## Version History

Introduced in R2006b

expand all

Warns starting in R2022a

Behavior changed in R2021b