This function decides whether the vertices of a network can be mapped to two vertex types in a way that no vertices of the same type are connected.

## Value

A named list with two elements:

- res
A logical scalar,

`TRUE`

if the can be bipartite,`FALSE`

otherwise.- type
A possible vertex type mapping, a logical vector. If no such mapping exists, then an empty vector.

## Details

A bipartite graph in igraph has a ‘`type`

’ vertex attribute
giving the two vertex types.

This function simply checks whether a graph *could* be bipartite. It
tries to find a mapping that gives a possible division of the vertices into
two classes, such that no two vertices of the same class are connected by an
edge.

The existence of such a mapping is equivalent of having no circuits of odd length in the graph. A graph with loop edges cannot bipartite.

Note that the mapping is not necessarily unique, e.g. if the graph has at least two components, then the vertices in the separate components can be mapped independently.

## See also

Bipartite graphs
`bipartite_projection()`

,
`is_bipartite()`

## Author

Gabor Csardi csardi.gabor@gmail.com

## Examples

```
## Rings with an even number of vertices are bipartite
g <- make_ring(10)
bipartite_mapping(g)
#> $res
#> [1] TRUE
#>
#> $type
#> [1] FALSE TRUE FALSE TRUE FALSE TRUE FALSE TRUE FALSE TRUE
#>
## All star graphs are bipartite
g2 <- make_star(10)
bipartite_mapping(g2)
#> $res
#> [1] TRUE
#>
#> $type
#> [1] FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
#>
## A graph containing a triangle is not bipartite
g3 <- make_ring(10)
g3 <- add_edges(g3, c(1, 3))
bipartite_mapping(g3)
#> $res
#> [1] FALSE
#>
#> $type
#> logical(0)
#>
```