Assign i.i.d. signed weights on a binary undirected adjacency

For each undirected edge, draws an inhibitory versus activatory sign and a common magnitude. By convention a positive precision off-diagonal is an inhibitory partial correlation (\(\rho_{jk\mid -\{j,k\}}=-\Omega_{jk}/ \sqrt{\Omega_{jj}\Omega_{kk}}\)). Thus prop_inhibitory is the target fraction of edges with \(\Omega_{jk}>0\) (negative partial correlation). The complementary fraction is activatory (\(\Omega_{jk}<0\)).

Usage

assign_iid_signed_weights(
  adjacency_matrix,
  prop_inhibitory = 0.5,
  weight_magnitude = 0.3
)

Arguments

adjacency_matrix

Symmetric binary matrix.

prop_inhibitory

Numeric in \([0,1]\); expected fraction of inhibitory precision edges.

weight_magnitude

Positive magnitude \(v\) for every signed off-diagonal.

Value

Symmetric numeric matrix with the same support as adjacency_matrix and zero diagonal.

Examples

A <- generate_random_network_skeleton(6L, "hub")
assign_iid_signed_weights(A, prop_inhibitory = 0.5)
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]  0.0  0.3 -0.3  0.0  0.0  0.0
#> [2,]  0.3  0.0  0.0  0.0  0.0  0.0
#> [3,] -0.3  0.0  0.0  0.0  0.0  0.0
#> [4,]  0.0  0.0  0.0  0.0  0.3 -0.3
#> [5,]  0.0  0.0  0.0  0.3  0.0  0.0
#> [6,]  0.0  0.0  0.0 -0.3  0.0  0.0