Builds the supra-adjacency matrix of a multilayer network. The diagonal blocks hold the intra-layer adjacencies and the off-diagonal blocks the inter-layer coupling.
Arguments
- layers
List of adjacency matrices (same dimensions)
- omega
Inter-layer coupling coefficient, a scalar or an L x L matrix. Default 1. For a matrix, entry
[a, b]witha < bsets the coupling of layers a and b.- coupling
Coupling type.
"diagonal"(default) couples each node to its own copy in the other layers with weightomega."full"couples every node to every node of the other layers with weightomega."custom"usesinterlayer_matrices.- interlayer_matrices
For
coupling = "custom", a list of inter-layer matrices. Accepted shapes:Named list with keys
"a_b"(integer layer indices) or"<layer_name_a>_<layer_name_b>"; either order works.Unnamed list of length
choose(L, 2)giving every pair in upper-triangle row-major order:(1,2), (1,3), ..., (1,L), (2,3), ..., (L-1,L).Unnamed list of length
L-1giving adjacent pairs only. Entryiis the coupling for(i, i+1).
The block of layers b and a is the transpose of the block of a and b. A pair with no matching entry receives the diagonal coupling
omega[a,b] * Iwith a warning. ANULLvalue withcoupling = "custom"is an error.
Value
A supra-adjacency matrix of dimension (NL) x (NL) with class
c("supra_adjacency", "matrix"). Diagonal N x N blocks hold the
intra-layer adjacencies and off-diagonal blocks the inter-layer coupling.
The attributes "n_nodes", "n_layers", "node_names",
"layer_names", "omega" and "coupling" record the
construction and are read back by supra_layer() and
supra_interlayer().
Examples
layers <- list(forward = regulation_net, backward = t(regulation_net))
supra_adjacency(layers, omega = 0.5)
#> forward_Explore forward_Plan forward_Monitor forward_Adapt
#> forward_Explore 0.00 0.00 0.00 0.00
#> forward_Plan 0.00 0.00 0.13 0.00
#> forward_Monitor 0.00 0.00 0.00 0.16
#> forward_Adapt 0.28 0.00 0.00 0.00
#> forward_Reflect 0.05 0.00 0.15 0.00
#> forward_Discuss 0.30 0.00 0.00 0.00
#> forward_Synthesize 0.00 0.11 0.07 0.00
#> forward_Evaluate 0.00 0.00 0.33 0.43
#> forward_Create 0.14 0.00 0.17 0.00
#> forward_Share 0.00 0.21 0.49 0.39
#> backward_Explore 0.50 0.00 0.00 0.00
#> backward_Plan 0.00 0.50 0.00 0.00
#> backward_Monitor 0.00 0.00 0.50 0.00
#> backward_Adapt 0.00 0.00 0.00 0.50
#> backward_Reflect 0.00 0.00 0.00 0.00
#> backward_Discuss 0.00 0.00 0.00 0.00
#> backward_Synthesize 0.00 0.00 0.00 0.00
#> backward_Evaluate 0.00 0.00 0.00 0.00
#> backward_Create 0.00 0.00 0.00 0.00
#> backward_Share 0.00 0.00 0.00 0.00
#> forward_Reflect forward_Discuss forward_Synthesize
#> forward_Explore 0.35 0.00 0.00
#> forward_Plan 0.00 0.40 0.00
#> forward_Monitor 0.00 0.00 0.00
#> forward_Adapt 0.00 0.34 0.17
#> forward_Reflect 0.00 0.00 0.00
#> forward_Discuss 0.35 0.00 0.00
#> forward_Synthesize 0.42 0.00 0.00
#> forward_Evaluate 0.07 0.00 0.00
#> forward_Create 0.00 0.00 0.00
#> forward_Share 0.00 0.00 0.00
#> backward_Explore 0.00 0.00 0.00
#> backward_Plan 0.00 0.00 0.00
#> backward_Monitor 0.00 0.00 0.00
#> backward_Adapt 0.00 0.00 0.00
#> backward_Reflect 0.50 0.00 0.00
#> backward_Discuss 0.00 0.50 0.00
#> backward_Synthesize 0.00 0.00 0.50
#> backward_Evaluate 0.00 0.00 0.00
#> backward_Create 0.00 0.00 0.00
#> backward_Share 0.00 0.00 0.00
#> forward_Evaluate forward_Create forward_Share
#> forward_Explore 0.00 0.00 0.27
#> forward_Plan 0.49 0.20 0.36
#> forward_Monitor 0.00 0.37 0.00
#> forward_Adapt 0.00 0.00 0.00
#> forward_Reflect 0.00 0.00 0.00
#> forward_Discuss 0.00 0.14 0.00
#> forward_Synthesize 0.00 0.00 0.00
#> forward_Evaluate 0.00 0.00 0.00
#> forward_Create 0.39 0.00 0.23
#> forward_Share 0.00 0.00 0.00
#> backward_Explore 0.00 0.00 0.00
#> backward_Plan 0.00 0.00 0.00
#> backward_Monitor 0.00 0.00 0.00
#> backward_Adapt 0.00 0.00 0.00
#> backward_Reflect 0.00 0.00 0.00
#> backward_Discuss 0.00 0.00 0.00
#> backward_Synthesize 0.00 0.00 0.00
#> backward_Evaluate 0.50 0.00 0.00
#> backward_Create 0.00 0.50 0.00
#> backward_Share 0.00 0.00 0.50
#> backward_Explore backward_Plan backward_Monitor
#> forward_Explore 0.50 0.00 0.00
#> forward_Plan 0.00 0.50 0.00
#> forward_Monitor 0.00 0.00 0.50
#> forward_Adapt 0.00 0.00 0.00
#> forward_Reflect 0.00 0.00 0.00
#> forward_Discuss 0.00 0.00 0.00
#> forward_Synthesize 0.00 0.00 0.00
#> forward_Evaluate 0.00 0.00 0.00
#> forward_Create 0.00 0.00 0.00
#> forward_Share 0.00 0.00 0.00
#> backward_Explore 0.00 0.00 0.00
#> backward_Plan 0.00 0.00 0.00
#> backward_Monitor 0.00 0.13 0.00
#> backward_Adapt 0.00 0.00 0.16
#> backward_Reflect 0.35 0.00 0.00
#> backward_Discuss 0.00 0.40 0.00
#> backward_Synthesize 0.00 0.00 0.00
#> backward_Evaluate 0.00 0.49 0.00
#> backward_Create 0.00 0.20 0.37
#> backward_Share 0.27 0.36 0.00
#> backward_Adapt backward_Reflect backward_Discuss
#> forward_Explore 0.00 0.00 0.00
#> forward_Plan 0.00 0.00 0.00
#> forward_Monitor 0.00 0.00 0.00
#> forward_Adapt 0.50 0.00 0.00
#> forward_Reflect 0.00 0.50 0.00
#> forward_Discuss 0.00 0.00 0.50
#> forward_Synthesize 0.00 0.00 0.00
#> forward_Evaluate 0.00 0.00 0.00
#> forward_Create 0.00 0.00 0.00
#> forward_Share 0.00 0.00 0.00
#> backward_Explore 0.28 0.05 0.30
#> backward_Plan 0.00 0.00 0.00
#> backward_Monitor 0.00 0.15 0.00
#> backward_Adapt 0.00 0.00 0.00
#> backward_Reflect 0.00 0.00 0.35
#> backward_Discuss 0.34 0.00 0.00
#> backward_Synthesize 0.17 0.00 0.00
#> backward_Evaluate 0.00 0.00 0.00
#> backward_Create 0.00 0.00 0.14
#> backward_Share 0.00 0.00 0.00
#> backward_Synthesize backward_Evaluate backward_Create
#> forward_Explore 0.00 0.00 0.00
#> forward_Plan 0.00 0.00 0.00
#> forward_Monitor 0.00 0.00 0.00
#> forward_Adapt 0.00 0.00 0.00
#> forward_Reflect 0.00 0.00 0.00
#> forward_Discuss 0.00 0.00 0.00
#> forward_Synthesize 0.50 0.00 0.00
#> forward_Evaluate 0.00 0.50 0.00
#> forward_Create 0.00 0.00 0.50
#> forward_Share 0.00 0.00 0.00
#> backward_Explore 0.00 0.00 0.14
#> backward_Plan 0.11 0.00 0.00
#> backward_Monitor 0.07 0.33 0.17
#> backward_Adapt 0.00 0.43 0.00
#> backward_Reflect 0.42 0.07 0.00
#> backward_Discuss 0.00 0.00 0.00
#> backward_Synthesize 0.00 0.00 0.00
#> backward_Evaluate 0.00 0.00 0.39
#> backward_Create 0.00 0.00 0.00
#> backward_Share 0.00 0.00 0.23
#> backward_Share
#> forward_Explore 0.00
#> forward_Plan 0.00
#> forward_Monitor 0.00
#> forward_Adapt 0.00
#> forward_Reflect 0.00
#> forward_Discuss 0.00
#> forward_Synthesize 0.00
#> forward_Evaluate 0.00
#> forward_Create 0.00
#> forward_Share 0.50
#> backward_Explore 0.00
#> backward_Plan 0.21
#> backward_Monitor 0.49
#> backward_Adapt 0.39
#> backward_Reflect 0.00
#> backward_Discuss 0.00
#> backward_Synthesize 0.00
#> backward_Evaluate 0.00
#> backward_Create 0.00
#> backward_Share 0.00
#> attr(,"n_nodes")
#> [1] 10
#> attr(,"n_layers")
#> [1] 2
#> attr(,"node_names")
#> [1] "Explore" "Plan" "Monitor" "Adapt" "Reflect"
#> [6] "Discuss" "Synthesize" "Evaluate" "Create" "Share"
#> attr(,"layer_names")
#> [1] "forward" "backward"
#> attr(,"omega")
#> [1] 0.5
#> attr(,"coupling")
#> [1] "diagonal"
#> attr(,"class")
#> [1] "supra_adjacency" "matrix"