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#' Is the graph a directed acyclic graph?
#'
#' @description
#'
#' Provides a logical value on whether the graph is a directed acyclic graph
#' (DAG). The conditions for a graph that is a DAG are that it should be a
#' directed graph and it should not contain any cycles.
#'
#' @inheritParams render_graph
#'
#' @return A logical value.
#'
#' @examples
#' # Create a directed graph containing
#' # only a balanced tree
#' graph_tree <-
#' create_graph() %>%
#' add_balanced_tree(
#' k = 2, h = 3)
#'
#' # Determine whether this graph
#' # is a DAG
#' graph_tree %>%
#' is_graph_dag()
#'
#' # Create a directed graph containing
#' # a single cycle
#' graph_cycle <-
#' create_graph() %>%
#' add_cycle(n = 5)
#'
#' # Determine whether this graph
#' # is a DAG
#' graph_cycle %>%
#' is_graph_dag()
#'
#' # Create an undirected graph
#' # containing a balanced tree
#' graph_tree_undirected <-
#' create_graph(
#' directed = FALSE) %>%
#' add_balanced_tree(
#' k = 2, h = 2)
#'
#' # Determine whether this graph
#' # is a DAG
#' graph_tree_undirected %>%
#' is_graph_dag()
#'
#' @export
is_graph_dag <- function(graph) {
# Validation: Graph object is valid
check_graph_valid(graph)
# If the graph contains no nodes, it
# cannot be a DAG
if (nrow(graph$nodes_df) == 0) {
return(FALSE)
}
# Convert the graph to an igraph object
ig_graph <- to_igraph(graph)
# Determine whether the graph is
# a simple graph
igraph::is_dag(ig_graph)
}
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