igraph (version 1.3.5)

bipartite_mapping: 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)

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.

Arguments

graph

The input graph.

Author

Gabor Csardi

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.

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)