Build a Simplicial Complex

Constructs a simplicial complex from a network or higher-order pathway object. Three construction methods are available:

• Clique complex ("clique"): every clique in the thresholded graph becomes a simplex. The standard bridge from graph theory to algebraic topology.

• Pathway complex ("pathway"): each higher-order pathway from a net_hon or net_hypa becomes a simplex.

• Vietoris-Rips ("vr"): nodes with edge weight \(\geq\) threshold are connected; all cliques in the resulting graph become simplices.

Usage

build_simplicial(
  x,
  type = "clique",
  threshold = 0,
  max_dim = 10L,
  max_pathways = NULL,
  ...
)

Arguments

x

A square matrix, tna, netobject, net_hon, or net_hypa.

type

Construction type: "clique" (default), "pathway", or "vr".

threshold

Minimum absolute edge weight to include an edge (default 0). Edges below this are ignored.

max_dim

Maximum simplex dimension (default 10). A k-simplex has k+1 nodes.

max_pathways

For type = "pathway": maximum number of pathways to include, ranked by count (HON) or ratio (HYPA). NULL includes all. Default NULL.

...

Additional arguments passed to build_hon() when x is a tna/netobject with type = "pathway".

Value

A simplicial_complex object.

See also

betti_numbers, persistent_homology, simplicial_degree, q_analysis

Examples

# \donttest{
seqs <- data.frame(
  V1 = sample(LETTERS[1:4], 30, TRUE), V2 = sample(LETTERS[1:4], 30, TRUE),
  V3 = sample(LETTERS[1:4], 30, TRUE), V4 = sample(LETTERS[1:4], 30, TRUE)
)
net <- build_network(seqs, method = "relative")
sc <- build_simplicial(net, threshold = 0.05)
print(sc)
#> Clique Complex 
#>   4 nodes, 15 simplices, dimension 3
#>   Density: 100.0%  |  Mean dim: 1.13  |  Euler: 1
#>   f-vector: (f0=4 f1=6 f2=4 f3=1)
#>   Betti: b0=1
#>   Nodes: A, B, C, D 
betti_numbers(sc)
#> b0 b1 b2 b3 
#>  1  0  0  0 
# }