test_that("update_ancestor_matrix computes correct transitive closure", {
  # Chain: node 1 (root) -> node 2 -> node 3
  # incid_matrix[i, j] == 1 means node j is a parent of node i
  incid_matrix <- matrix(0, nrow = 3, ncol = 3)
  incid_matrix[2, 1] <- 1 # node 1 is a parent of node 2
  incid_matrix[3, 2] <- 1 # node 2 is a parent of node 3

  ances <- update_ancestor_matrix(incid_matrix)

  expect_equal(ances[2, 1], 1)
  expect_equal(ances[3, 2], 1)
  expect_equal(ances[3, 1], 1) # transitive: node 1 is an ancestor of node 3
  expect_equal(sum(diag(ances)), 0) # should be acyclic and have no self-ancestry
})

test_that("check_ances_matrix detects a directed cycle", {
  # 2-node cycle: 1 -> 2 -> 1
  incid_matrix <- matrix(c(0, 1, 1, 0), nrow = 2, byrow = TRUE)
  ances <- update_ancestor_matrix(incid_matrix)

  expect_gt(check_ances_matrix(ances), 0)
})

test_that("check_ances_matrix reports zero loops for a valid DAG", {
  incid_matrix <- matrix(0, nrow = 3, ncol = 3)
  incid_matrix[2, 1] <- 1
  incid_matrix[3, 2] <- 1
  ances <- update_ancestor_matrix(incid_matrix)

  expect_equal(check_ances_matrix(ances), 0)
})

test_that("GenerateNetwork always produces an acyclic topology", {
  set.seed(1)
  net <- GenerateNetwork(num.node = 8)
  incid <- (net > 0) * 1
  ances <- update_ancestor_matrix(incid)

  expect_equal(check_ances_matrix(ances), 0)
})