This function transforms an adjacency matrix into an incidence matrix.
Arguments
- A
A square numeric matrix representing the adjacency matrix of a graph. The matrix should have non-negative values, where `A[i, j]` represents the weight of the edge from node `i` to node `j`.
- loops
Logical. If `TRUE`, self-loops (edges from a node to itself) are included in the incidence matrix. If `FALSE`, they are removed. Default is `TRUE`.
- directed
Logical. If `TRUE`, the graph is treated as directed, meaning each edge has a specific source and target. If `FALSE`, the graph is treated as undirected, and edges are symmetrically represented. Default is `TRUE`.
- weighted
Logical. If `TRUE`, edge weights from `A` are included in the incidence matrix. If `FALSE`, all edges are treated as having weight `1`. Default is `TRUE`.
Value
A numeric matrix where rows represent nodes and columns represent edges. - In a **directed** network, a source node has a negative value (-weight), and a target node has a positive value (+weight). - In an **undirected** network, both nodes involved in an edge share the weight (positive values). - If `weighted = FALSE`, all edges have a weight of `1`.
Examples
# Define an adjacency matrix (directed and weighted)
A <- matrix(c(
1, 3, 0, 0, 2,
0, 0, 2, 0, 0,
5, 0, 0, 0, 0,
0, 0, 0, 0, 1,
0, 4, 0, 0, 0
), byrow = TRUE, nrow = 5)
# Convert to an incidence matrix (directed, weighted)
(inc_matrix <- adj_to_incidence(A))
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 1 5 -3 0 0 -2 0
#> [2,] 0 0 3 4 -2 0 0
#> [3,] 0 -5 0 0 2 0 0
#> [4,] 0 0 0 0 0 0 -1
#> [5,] 0 0 0 -4 0 2 1
# Undirected, weighted graph
(inc_matrix_undirected <- adj_to_incidence(A, directed = FALSE))
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1 3 0 2 0
#> [2,] 0 3 2 0 0
#> [3,] 0 0 2 0 0
#> [4,] 0 0 0 0 1
#> [5,] 0 0 0 2 1
# Directed, unweighted graph
(inc_matrix_unweighted <- adj_to_incidence(A, weighted = FALSE))
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 1 1 -1 0 0 -1 0
#> [2,] 0 0 1 1 -1 0 0
#> [3,] 0 -1 0 0 1 0 0
#> [4,] 0 0 0 0 0 0 -1
#> [5,] 0 0 0 -1 0 1 1
# Ignore loops
(inc_matrix_no_loops <- adj_to_incidence(A, loops = FALSE))
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 5 -3 0 0 -2 0
#> [2,] 0 3 4 -2 0 0
#> [3,] -5 0 0 2 0 0
#> [4,] 0 0 0 0 0 -1
#> [5,] 0 0 -4 0 2 1