project_bipartite: Project Bipartite Network to One-Mode

In cograph: Analysis and Visualization of Complex Networks

Project Bipartite Network to One-Mode

Description

Projects a two-mode (bipartite/incidence) network into a one-mode adjacency matrix. Row-mode projection yields a matrix of shared-column connections among row nodes; column-mode projection does the converse.

Usage

project_bipartite(x, mode = "rows", method = "sum", ...)

Arguments

x	An incidence matrix (rows = type 1 nodes, columns = type 2 nodes) where non-zero entries indicate connections. Can also be a data.frame with columns type1, type2, and optionally weight.
mode	Character. "rows" (default) projects onto row nodes (result: n_rows x n_rows). "columns" projects onto column nodes (result: n_cols x n_cols).
method	Character. Projection method: "sum" Weighted projection: A %*% t(A) (rows) or t(A) %*% A (columns). Edge weight equals sum of shared connection-weight products. "binary" Co-occurrence count: binarize A first, then compute overlap. Edge weight equals number of shared connections. "jaccard" Jaccard similarity: shared / (total_i + total_j - shared) for each pair. "cosine" Cosine similarity: dot product of row (or column) vectors divided by the product of their norms. "newman" Newman's weighted projection (Newman 2001): each shared affiliation contributes 1 / (d_k - 1) where d_k is the degree of the shared node. Gives more weight to connections through exclusive affiliations.
...	Additional arguments (currently unused).

Details

Only method = "sum" and method = "cosine" use the incidence values themselves. "binary", "jaccard" and "newman" first binarize the incidence matrix (x > 0), so any weights are discarded for those three.

For the Newman projection, affiliations shared with only one node of the focal type (d_k = 1) are skipped, since 1 / (d_k - 1) is undefined. This follows the convention in Newman (2001).

Value

A square adjacency matrix, one row and column per node of the projected mode: n_rows x n_rows named by rownames(x) for mode = "rows", n_cols x n_cols named by colnames(x) for mode = "columns". The diagonal is set to 0 (no self-loops).

References

Newman, M. E. J. (2001). Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. Physical Review E, 64(1), 016132.

See Also

is_bipartite, plot_heatmap

Examples

# Incidence matrix: 4 students x 3 courses
inc <- matrix(c(1, 1, 0,
                1, 0, 1,
                0, 1, 1,
                1, 1, 1), 4, 3, byrow = TRUE)
rownames(inc) <- paste0("S", 1:4)
colnames(inc) <- paste0("C", 1:3)

# Student co-enrollment (weighted)
cograph::project_bipartite(inc, mode = "rows", method = "sum")

# Course overlap (Jaccard similarity)
cograph::project_bipartite(inc, mode = "columns", method = "jaccard")

# Newman's weighted projection
cograph::project_bipartite(inc, mode = "rows", method = "newman")

cograph documentation built on Sept. 30, 2026, 5:08 p.m.