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Convert an Adjacency Matrix to an Incidence Matrix

Source: R/utilities.R
adj_to_incidence.Rd

This function transforms an adjacency matrix into an incidence matrix.

Usage

adj_to_incidence(A, loops = TRUE, directed = TRUE, weighted = TRUE)

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->1 3->1 1->2 5->2 2->3 1->5 4->5
#> 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))
#>   1-1 1-2 1-3 2-3 1-5 2-5 4-5
#> 1   1   3   5   0   2   0   0
#> 2   0   3   0   2   0   4   0
#> 3   0   0   5   2   0   0   0
#> 4   0   0   0   0   0   0   1
#> 5   0   0   0   0   2   4   1

# Directed, unweighted graph
(inc_matrix_unweighted <- adj_to_incidence(A, weighted = FALSE))
#>   1->1 3->1 1->2 5->2 2->3 1->5 4->5
#> 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))
#>   3->1 1->2 5->2 2->3 1->5 4->5
#> 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