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//! Regularity check (ALGO-PR-070).
//!
//! A graph is *k-regular* if every vertex has the same degree *k*.
//! For directed graphs, a graph is regular if every vertex has the
//! same out-degree AND the same in-degree (not necessarily equal to
//! each other).
use crate::algorithms::properties::degree::{DegreeMode, degree_sequence};
use crate::core::{Graph, IgraphResult};
/// Check whether a graph is regular.
///
/// A graph is regular if every vertex has the same degree. For
/// directed graphs, this checks that all out-degrees are equal AND
/// all in-degrees are equal.
///
/// An empty graph (0 vertices) is considered regular.
/// A graph with one vertex is regular (degree may be nonzero due to
/// self-loops).
///
/// # Examples
///
/// ```
/// use rust_igraph::{Graph, is_regular};
///
/// // Cycle C4 is 2-regular
/// 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();
/// g.add_edge(3, 0).unwrap();
/// assert!(is_regular(&g).unwrap());
///
/// // Path P3 is not regular (endpoints have degree 1, middle has 2)
/// let mut g = Graph::with_vertices(3);
/// g.add_edge(0, 1).unwrap();
/// g.add_edge(1, 2).unwrap();
/// assert!(!is_regular(&g).unwrap());
/// ```
pub fn is_regular(graph: &Graph) -> IgraphResult<bool> {
let n = graph.vcount();
if n <= 1 {
return Ok(true);
}
let out_deg = degree_sequence(graph, DegreeMode::Out)?;
if out_deg.windows(2).any(|w| w[0] != w[1]) {
return Ok(false);
}
if graph.is_directed() {
let in_deg = degree_sequence(graph, DegreeMode::In)?;
if in_deg.windows(2).any(|w| w[0] != w[1]) {
return Ok(false);
}
}
Ok(true)
}
/// Return the regularity degree of the graph, or `None` if the graph
/// is not regular.
///
/// For undirected graphs, returns the common degree. For directed
/// graphs, returns the common out-degree (which equals the common
/// in-degree in a regular directed graph where out-degree == in-degree
/// for all vertices; if out-degrees are all equal and in-degrees are
/// all equal but differ from each other, returns `None` since such a
/// graph is not considered regular in the standard sense for simple
/// regularity queries).
///
/// An empty graph returns `None` (no vertices, no degree).
///
/// # Examples
///
/// ```
/// use rust_igraph::{Graph, regularity};
///
/// // K3 is 2-regular
/// 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_eq!(regularity(&g).unwrap(), Some(2));
///
/// // Star graph is not regular
/// 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_eq!(regularity(&g).unwrap(), None);
/// ```
pub fn regularity(graph: &Graph) -> IgraphResult<Option<u32>> {
let n = graph.vcount();
if n == 0 {
return Ok(None);
}
let out_deg = degree_sequence(graph, DegreeMode::Out)?;
if out_deg.windows(2).any(|w| w[0] != w[1]) {
return Ok(None);
}
if graph.is_directed() {
let in_deg = degree_sequence(graph, DegreeMode::In)?;
if in_deg.windows(2).any(|w| w[0] != w[1]) {
return Ok(None);
}
if out_deg[0] != in_deg[0] {
return Ok(None);
}
}
Ok(Some(out_deg[0]))
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn empty_graph_is_regular() {
let g = Graph::with_vertices(0);
assert!(is_regular(&g).unwrap());
}
#[test]
fn empty_graph_regularity_none() {
let g = Graph::with_vertices(0);
assert_eq!(regularity(&g).unwrap(), None);
}
#[test]
fn single_vertex_no_edges() {
let g = Graph::with_vertices(1);
assert!(is_regular(&g).unwrap());
assert_eq!(regularity(&g).unwrap(), Some(0));
}
#[test]
fn single_vertex_self_loop() {
let mut g = Graph::with_vertices(1);
g.add_edge(0, 0).unwrap();
assert!(is_regular(&g).unwrap());
}
#[test]
fn two_vertices_no_edges() {
let g = Graph::with_vertices(2);
assert!(is_regular(&g).unwrap());
assert_eq!(regularity(&g).unwrap(), Some(0));
}
#[test]
fn single_edge() {
let mut g = Graph::with_vertices(2);
g.add_edge(0, 1).unwrap();
assert!(is_regular(&g).unwrap());
assert_eq!(regularity(&g).unwrap(), Some(1));
}
#[test]
fn path_3_not_regular() {
let mut g = Graph::with_vertices(3);
g.add_edge(0, 1).unwrap();
g.add_edge(1, 2).unwrap();
assert!(!is_regular(&g).unwrap());
assert_eq!(regularity(&g).unwrap(), None);
}
#[test]
fn triangle_is_2_regular() {
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_regular(&g).unwrap());
assert_eq!(regularity(&g).unwrap(), Some(2));
}
#[test]
fn cycle_4_is_2_regular() {
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();
g.add_edge(3, 0).unwrap();
assert!(is_regular(&g).unwrap());
assert_eq!(regularity(&g).unwrap(), Some(2));
}
#[test]
fn complete_k4_is_3_regular() {
let mut g = Graph::with_vertices(4);
for u in 0..4u32 {
for v in (u + 1)..4 {
g.add_edge(u, v).unwrap();
}
}
assert!(is_regular(&g).unwrap());
assert_eq!(regularity(&g).unwrap(), Some(3));
}
#[test]
fn star_not_regular() {
let mut g = Graph::with_vertices(5);
for i in 1..5u32 {
g.add_edge(0, i).unwrap();
}
assert!(!is_regular(&g).unwrap());
assert_eq!(regularity(&g).unwrap(), None);
}
#[test]
fn petersen_is_3_regular() {
let mut g = Graph::with_vertices(10);
let edges = [
(0, 1),
(1, 2),
(2, 3),
(3, 4),
(4, 0),
(5, 7),
(7, 9),
(9, 6),
(6, 8),
(8, 5),
(0, 5),
(1, 6),
(2, 7),
(3, 8),
(4, 9),
];
for (u, v) in edges {
g.add_edge(u, v).unwrap();
}
assert!(is_regular(&g).unwrap());
assert_eq!(regularity(&g).unwrap(), Some(3));
}
#[test]
fn directed_cycle_is_regular() {
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_regular(&g).unwrap());
assert_eq!(regularity(&g).unwrap(), Some(1));
}
#[test]
fn directed_unequal_in_out_not_regular() {
let mut g = Graph::new(3, true).unwrap();
g.add_edge(0, 1).unwrap();
g.add_edge(0, 2).unwrap();
g.add_edge(1, 2).unwrap();
assert!(!is_regular(&g).unwrap());
assert_eq!(regularity(&g).unwrap(), None);
}
#[test]
fn parallel_edges_regular() {
let mut g = Graph::with_vertices(2);
g.add_edge(0, 1).unwrap();
g.add_edge(0, 1).unwrap();
assert!(is_regular(&g).unwrap());
assert_eq!(regularity(&g).unwrap(), Some(2));
}
#[test]
fn bipartite_k22_is_2_regular() {
let mut g = Graph::with_vertices(4);
g.add_edge(0, 2).unwrap();
g.add_edge(0, 3).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(1, 3).unwrap();
assert!(is_regular(&g).unwrap());
assert_eq!(regularity(&g).unwrap(), Some(2));
}
}