Euler Characteristic

Computes \(\chi = \sum_{k=0}^{d} (-1)^k f_k\) where \(f_k\) is the number of k-simplices. By the Euler-Poincare theorem, \(\chi = \sum_{k} (-1)^k \beta_k\).

Usage

euler_characteristic(sc)

Arguments

sc

A simplicial_complex object.

Value

Integer.

Examples

# \donttest{
mat <- matrix(c(0,.6,.5,.6,0,.4,.5,.4,0), 3, 3)
colnames(mat) <- rownames(mat) <- c("A","B","C")
sc <- build_simplicial(mat, threshold = 0.3)
euler_characteristic(sc)
#> [1] 1
# }