# bipartite_mapping: Decide whether a graph is bipartite In igraph: Network Analysis and Visualization

 bipartite_mapping R Documentation

## Decide whether a graph is bipartite

### Description

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.

### Usage

``````bipartite_mapping(graph)
``````

### Arguments

 `graph` The input graph.

### 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.

### 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.

### Author(s)

Gabor Csardi csardi.gabor@gmail.com

Bipartite graphs `bipartite_projection()`, `is_bipartite()`

### Examples

``````
## Rings with an even number of vertices are bipartite
g <- make_ring(10)
bipartite_mapping(g)

## All star graphs are bipartite
g2 <- make_star(10)
bipartite_mapping(g2)

## A graph containing a triangle is not bipartite
g3 <- make_ring(10)
g3 <- add_edges(g3, c(1, 3))
bipartite_mapping(g3)
``````

igraph documentation built on Aug. 10, 2023, 9:08 a.m.