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//! Diamond-free graph predicate (ALGO-PR-097).
//!
//! A graph is diamond-free if it contains no induced subgraph
//! isomorphic to the diamond graph (`K_4` minus one edge, also
//! denoted `K_4^-`). The diamond has 4 vertices and 5 edges.
//!
//! For directed graphs, the function returns `false`.
use crate::core::{Graph, IgraphResult};
/// Check whether a graph is diamond-free.
///
/// A diamond-free graph has no induced `K_4` minus one edge. The
/// diamond has vertices {a, b, c, d} with edges {ab, ac, ad, bc, bd}
/// (c and d not adjacent).
///
/// Returns `false` for directed graphs.
///
/// # Examples
///
/// ```
/// use rust_igraph::{Graph, is_diamond_free};
///
/// // Triangle is diamond-free
/// 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_diamond_free(&g).unwrap());
///
/// // Diamond: `K_4` minus edge 2-3
/// 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();
/// assert!(!is_diamond_free(&g).unwrap());
/// ```
pub fn is_diamond_free(graph: &Graph) -> IgraphResult<bool> {
if graph.is_directed() {
return Ok(false);
}
let n = graph.vcount();
if n <= 3 {
return Ok(true);
}
// Build adjacency for fast pair lookup
let n_usize = n as usize;
let mut adj = vec![vec![false; n_usize]; n_usize];
for v in 0..n {
let nbrs = graph.neighbors(v)?;
for &w in &nbrs {
adj[v as usize][w as usize] = true;
}
}
// A diamond is formed when an edge (u, v) has two or more common
// neighbors c1, c2 such that c1 and c2 are NOT adjacent.
// If c1-c2 are adjacent, then {u, v, c1, c2} form K_4.
// If c1-c2 are non-adjacent, then {u, v, c1, c2} form a diamond.
//
// So: for each edge (u, v), find all common neighbors, and check
// if any pair among them is non-adjacent.
for u in 0..n {
let nbrs_u = graph.neighbors(u)?;
for &v in &nbrs_u {
if v <= u {
continue;
}
// Find common neighbors of u and v
let common: Vec<u32> = nbrs_u
.iter()
.filter(|&&w| w != v && adj[v as usize][w as usize])
.copied()
.collect();
// Check if any pair of common neighbors is non-adjacent
for i in 0..common.len() {
for j in (i + 1)..common.len() {
if !adj[common[i] as usize][common[j] as usize] {
return Ok(false);
}
}
}
}
}
Ok(true)
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn empty_graph() {
let g = Graph::with_vertices(0);
assert!(is_diamond_free(&g).unwrap());
}
#[test]
fn single_vertex() {
let g = Graph::with_vertices(1);
assert!(is_diamond_free(&g).unwrap());
}
#[test]
fn single_edge() {
let mut g = Graph::with_vertices(2);
g.add_edge(0, 1).unwrap();
assert!(is_diamond_free(&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_diamond_free(&g).unwrap());
}
#[test]
fn diamond() {
// K_4 minus edge 2-3: vertices {0,1,2,3}, edges {01,02,03,12,13}
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();
assert!(!is_diamond_free(&g).unwrap());
}
#[test]
fn k4_is_diamond_free() {
// K_4 is diamond-free: any 4 vertices induce K_4 (6 edges),
// not a diamond (5 edges)
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_diamond_free(&g).unwrap());
}
#[test]
fn path_diamond_free() {
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();
assert!(is_diamond_free(&g).unwrap());
}
#[test]
fn cycle_c5_diamond_free() {
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_diamond_free(&g).unwrap());
}
#[test]
fn star_diamond_free() {
let mut g = Graph::with_vertices(5);
g.add_edge(0, 1).unwrap();
g.add_edge(0, 2).unwrap();
g.add_edge(0, 3).unwrap();
g.add_edge(0, 4).unwrap();
assert!(is_diamond_free(&g).unwrap());
}
#[test]
fn two_triangles_sharing_vertex() {
// 0-1-2-0, 0-3-4-0
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(0, 3).unwrap();
g.add_edge(3, 4).unwrap();
g.add_edge(4, 0).unwrap();
// Vertex 0 connects to 1,2,3,4. Common neighbors of edge 0-1:
// just 2. Common neighbors of edge 0-3: just 4. No diamond.
assert!(is_diamond_free(&g).unwrap());
}
#[test]
fn two_triangles_sharing_edge() {
// 0-1-2-0, 0-1-3
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(0, 3).unwrap();
g.add_edge(1, 3).unwrap();
// Edge 0-1 has common neighbors 2 and 3.
// 2-3 not adjacent → diamond!
assert!(!is_diamond_free(&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_diamond_free(&g).unwrap());
}
#[test]
fn isolated_vertices() {
let g = Graph::with_vertices(10);
assert!(is_diamond_free(&g).unwrap());
}
#[test]
fn wheel_w5_not_diamond_free() {
// W_5: hub 0 connected to cycle 1-2-3-4-5-1
let mut g = Graph::with_vertices(6);
g.add_edge(0, 1).unwrap();
g.add_edge(0, 2).unwrap();
g.add_edge(0, 3).unwrap();
g.add_edge(0, 4).unwrap();
g.add_edge(0, 5).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(2, 3).unwrap();
g.add_edge(3, 4).unwrap();
g.add_edge(4, 5).unwrap();
g.add_edge(5, 1).unwrap();
// Edge 0-1 has common neighbors 2 and 5; 2-5 not adjacent → diamond
assert!(!is_diamond_free(&g).unwrap());
}
}