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//! Unicyclic graph predicate (ALGO-PR-093).
//!
//! A unicyclic graph is a connected graph containing exactly one
//! cycle. Equivalently, a connected graph with n vertices and n edges.
//!
//! For directed graphs, the function returns `false`.
use crate::algorithms::connectivity::{ConnectednessMode, is_connected};
use crate::core::{Graph, IgraphResult};
/// Check whether a graph is unicyclic.
///
/// A unicyclic graph is connected and has exactly as many edges as
/// vertices (n vertices, n edges), which means it contains exactly
/// one cycle.
///
/// Returns `false` for directed graphs, disconnected graphs, trees
/// (n-1 edges), and graphs with more than one cycle.
///
/// # Examples
///
/// ```
/// use rust_igraph::{Graph, is_unicyclic};
///
/// // Triangle with a tail: 0-1-2-0, 2-3
/// let mut g = Graph::with_vertices(4);
/// g.add_edge(0, 1).unwrap();
/// g.add_edge(1, 2).unwrap();
/// g.add_edge(2, 0).unwrap();
/// g.add_edge(2, 3).unwrap();
/// assert!(is_unicyclic(&g).unwrap());
///
/// // Path is NOT unicyclic (no cycle)
/// let mut g = Graph::with_vertices(3);
/// g.add_edge(0, 1).unwrap();
/// g.add_edge(1, 2).unwrap();
/// assert!(!is_unicyclic(&g).unwrap());
/// ```
pub fn is_unicyclic(graph: &Graph) -> IgraphResult<bool> {
if graph.is_directed() {
return Ok(false);
}
let n = graph.vcount();
if n == 0 {
return Ok(false);
}
// A connected graph with n edges has exactly one cycle.
if graph.ecount() != n as usize {
return Ok(false);
}
is_connected(graph, ConnectednessMode::Weak)
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn empty_graph() {
let g = Graph::with_vertices(0);
assert!(!is_unicyclic(&g).unwrap());
}
#[test]
fn single_vertex() {
let g = Graph::with_vertices(1);
assert!(!is_unicyclic(&g).unwrap());
}
#[test]
fn single_edge() {
let mut g = Graph::with_vertices(2);
g.add_edge(0, 1).unwrap();
assert!(!is_unicyclic(&g).unwrap());
}
#[test]
fn triangle() {
let mut g = Graph::with_vertices(3);
g.add_edge(0, 1).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(2, 0).unwrap();
assert!(is_unicyclic(&g).unwrap());
}
#[test]
fn c5() {
let mut g = Graph::with_vertices(5);
g.add_edge(0, 1).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(2, 3).unwrap();
g.add_edge(3, 4).unwrap();
g.add_edge(4, 0).unwrap();
assert!(is_unicyclic(&g).unwrap());
}
#[test]
fn triangle_with_tail() {
// 0-1-2-0, 2-3
let mut g = Graph::with_vertices(4);
g.add_edge(0, 1).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(2, 0).unwrap();
g.add_edge(2, 3).unwrap();
assert!(is_unicyclic(&g).unwrap());
}
#[test]
fn path_not_unicyclic() {
let mut g = Graph::with_vertices(4);
g.add_edge(0, 1).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(2, 3).unwrap();
assert!(!is_unicyclic(&g).unwrap());
}
#[test]
fn k4_not_unicyclic() {
// K4 has 6 edges, 4 vertices — multiple cycles
let mut g = Graph::with_vertices(4);
g.add_edge(0, 1).unwrap();
g.add_edge(0, 2).unwrap();
g.add_edge(0, 3).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(1, 3).unwrap();
g.add_edge(2, 3).unwrap();
assert!(!is_unicyclic(&g).unwrap());
}
#[test]
fn two_triangles_disconnected() {
// Two triangles, each unicyclic, but disconnected
let mut g = Graph::with_vertices(6);
g.add_edge(0, 1).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(2, 0).unwrap();
g.add_edge(3, 4).unwrap();
g.add_edge(4, 5).unwrap();
g.add_edge(5, 3).unwrap();
assert!(!is_unicyclic(&g).unwrap());
}
#[test]
fn theta_graph_not_unicyclic() {
// Theta: two paths between same endpoints → 2 cycles
// 0-1-2-3, 0-4-3: 5 vertices, 5 edges, connected
// Wait: 5 vertices, 5 edges, connected → exactly 1 cycle!
// Actually no: 0-1-2-3, 0-4-3, 0-3 would be theta.
// Let me make a proper graph with 2 cycles:
// Triangle 0-1-2 + triangle 0-2-3: 4 vertices, 5 edges
let mut g = Graph::with_vertices(4);
g.add_edge(0, 1).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(2, 0).unwrap();
g.add_edge(0, 3).unwrap();
g.add_edge(3, 2).unwrap();
// 4 vertices, 5 edges → not unicyclic
assert!(!is_unicyclic(&g).unwrap());
}
#[test]
fn directed_returns_false() {
let mut g = Graph::new(3, true).unwrap();
g.add_edge(0, 1).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(2, 0).unwrap();
assert!(!is_unicyclic(&g).unwrap());
}
#[test]
fn star_not_unicyclic() {
let mut g = Graph::with_vertices(4);
g.add_edge(0, 1).unwrap();
g.add_edge(0, 2).unwrap();
g.add_edge(0, 3).unwrap();
assert!(!is_unicyclic(&g).unwrap());
}
#[test]
fn lollipop() {
// Triangle 0-1-2-0 with a path tail 2-3-4
let mut g = Graph::with_vertices(5);
g.add_edge(0, 1).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(2, 0).unwrap();
g.add_edge(2, 3).unwrap();
g.add_edge(3, 4).unwrap();
assert!(is_unicyclic(&g).unwrap());
}
}