Check if a Matrix Could Be Bipartite

Tests whether a matrix could represent a bipartite incidence matrix. A non-square matrix is considered bipartite by default. For square matrices, checks whether the corresponding graph has bipartite structure (i.e., nodes can be partitioned into two groups with edges only between groups).

Usage

is_bipartite(x)

Arguments

x

A numeric matrix.

Value

Logical. TRUE if the matrix could represent a bipartite network, FALSE otherwise.

Details

For non-square matrices, returns TRUE since they naturally represent two-mode data (rows and columns are distinct node types).

For square matrices, the function checks whether the corresponding undirected graph is bipartite by attempting a two-coloring via igraph::bipartite_mapping() when igraph is available. Without igraph, it uses a breadth-first two-coloring. Positive entries define the edges, edge direction is ignored, and the diagonal (self-loops) is dropped before the check.

Examples

inc <- matrix(c(1, 0, 1, 1, 1, 0), 2, 3)
cograph::is_bipartite(inc)
#> [1] TRUE