Check if a Matrix Could Be Bipartite — is

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::is_bipartite() when igraph is available. Without igraph, it uses a BFS-based two-coloring algorithm.

Examples

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

# Square bipartite-compatible adjacency
adj <- matrix(c(0, 0, 1, 1,
                0, 0, 1, 0,
                1, 1, 0, 0,
                1, 0, 0, 0), 4, 4, byrow = TRUE)
cograph::is_bipartite(adj)
#> [1] TRUE

# Non-bipartite (triangle)
tri <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
cograph::is_bipartite(tri)
#> [1] FALSE