incidence matrix of simplexes or cliques
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.
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