Simplicial complexes — simplicial

incidence matrix of simplexes or cliques

Usage

simplicial_complexes(A, zero_simplex = FALSE, projection = FALSE)

Arguments

A: A symmetric matrix object.
zero_simplex: Whether to include the zero simple.
projection: Whether to return the links between actors (i.e., rows) through their shared linking events (i.e., columns).

Value

This function return an incidence matrix of actors participating in simplices or simplicial complexes

References

Atkin, R. H. (1974). Mathematical structure in human affairs. New York: Crane, Rusak.

Freeman, L. C. (1980). Q-analysis and the structure of friendship networks. International Journal of Man-Machine Studies, 12(4), 367–378. https://doi.org/10.1016/S0020-7373(80)80021-6

Wasserman, S. and Faust, K. (1994). Social network analysis: Methods and applications. Cambridge University Press.

Author

Alejandro Espinosa-Rada

Examples

A <- matrix(c(
  0, 1, 1, 0, 0, 0, 0, 1, 0,
  1, 0, 1, 0, 0, 0, 0, 0, 0,
  1, 1, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 1, 1, 0, 0, 0,
  0, 0, 0, 1, 0, 0, 0, 0, 0,
  0, 0, 0, 1, 0, 0, 1, 1, 0,
  0, 0, 0, 0, 0, 1, 0, 1, 0,
  1, 0, 0, 0, 0, 1, 1, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0
), byrow = TRUE, ncol = 9)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- rownames(A)
simplicial_complexes(A, zero_simplex = FALSE)
#>   1 2 3 4 5 6 7 8 9 10 11
#> a 1 0 0 0 1 1 1 0 0  0  0
#> b 1 0 0 0 1 0 0 1 0  0  0
#> c 1 0 0 0 0 1 0 1 0  0  0
#> d 0 0 0 0 0 0 0 0 1  1  0
#> e 0 0 0 0 0 0 0 0 1  0  0
#> f 0 1 0 1 0 0 0 0 0  1  1
#> g 0 0 1 1 0 0 0 0 0  0  1
#> h 0 1 1 1 0 0 1 0 0  0  0