Refactor generators tests and add missing tests

Reviewed-on: #10

Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name = "grapherity"
-version = "0.3.0"
+version = "0.3.1"
 authors = ["Stefan Müller"]
 edition = "2024"
 rust-version = "1.85.0"

src/generators.rs

@@ -1,6 +1,119 @@
 //! Generators for common graphs.
 
-use crate::traits::{GraphTopology, GraphTopologyAddition};
+use crate::models::AppendGraph;
+use crate::traits::{GraphTopology, GraphTopologyAddition, GraphTopologyConversion};
+
+/// Builds a graph of type `G` by running a generator on a temporary graph.
+///
+/// `generate_as` fills a temporary [`AppendGraph`] and converts it to `G`. It returns the handles
+/// of the elements it created as handles of the resulting graph. This makes it possible to obtain
+/// graph types directly that do not implement [`GraphTopologyAddition`], such as [`FrozenGraph`].
+///
+/// # Examples
+///
+/// ```
+/// use grapherity::prelude::*;
+/// use grapherity::generators;
+/// use grapherity::models::FrozenGraph;
+///
+/// // Generates a parameterless Petersen graph as a FrozenGraph model.
+/// let (graph, vertices, edges) = generators::generate_as::<FrozenGraph>(generators::petersen);
+/// assert_eq!(graph.vertex_count(), 10);
+/// assert!(graph.vertices().all(|v| graph.degree(v) == 3));
+///
+/// // Generates a parameterized complete graph as a FrozenGraph model.
+/// let (graph, vertices, edges) = generators::generate_as::<FrozenGraph>(|g| generators::complete(g, 5));
+/// assert_eq!(graph.vertex_count(), 5);
+/// assert!(graph.vertices().all(|v| graph.degree(v) == 4));
+/// ```
+///
+/// [`FrozenGraph`]: crate::models::FrozenGraph
+pub fn generate_as<G>(
+    generator: impl FnOnce(
+        &mut AppendGraph,
+    ) -> (
+        Vec<<AppendGraph as GraphTopology>::Vertex>,
+        Vec<<AppendGraph as GraphTopology>::Edge>,
+    ),
+) -> (G, Vec<G::Vertex>, Vec<G::Edge>)
+where
+    G: GraphTopologyConversion,
+{
+    let mut builder = AppendGraph::new();
+    let (vertices, edges) = generator(&mut builder);
+    let (graph, iso) = G::convert(&builder);
+    (
+        graph,
+        vertices.into_iter().map(|v| iso.vertex(v)).collect(),
+        edges.into_iter().map(|e| iso.edge(e)).collect(),
+    )
+}
+
+/// Generates a path graph.
+///
+/// Generates a [path graph] *P(n)* with `n` vertices and `n - 1` edges in `graph` as a new
+/// connected component and returns the new vertices *v0, v1, ..., v(n - 1)* and edges
+/// *e0, e1, ..., e(n - 2)* in order, i.e. *e0 = (v0, v1)*, *e1 = (v1, v2)*, etc. and *v0* and
+/// *v(n-1)* being the two terminal vertices
+///
+/// For `n == 0`, nothing is added. For `n == 1`, only a single vertex and no edges are added.
+///
+/// [Path graph]: https://en.wikipedia.org/wiki/Path_graph
+pub fn path<G: GraphTopologyAddition>(graph: &mut G, n: usize) -> (Vec<G::Vertex>, Vec<G::Edge>) {
+    let edge_capacity = n.saturating_sub(1);
+    graph.reserve_vertices(n);
+    graph.reserve_edges(edge_capacity);
+    let vertices: Vec<_> = (0..n).map(|_| graph.add_vertex()).collect();
+    let edges = (0..edge_capacity)
+        .map(|i| graph.add_edge(vertices[i], vertices[i + 1]))
+        .collect();
+    (vertices, edges)
+}
+
+/// Generates a cycle graph.
+///
+/// Generates a [cycle graph] *C(n)* with `n` vertices and `n` edges in `graph` as a new connected
+/// component and returns the new vertices *v0, v1, ..., v(n - 1)* and edges *e0, e1, ..., e(n - 1)*
+/// in order, i.e. *e0 = (v0, v1), e1 = (v1, v2), ..., e(n - 1) = (v(n - 1), v0)*.
+///
+/// For `n == 0`, nothing is added. For `n == 1`, a single vertex with a loop is added. For
+/// `n == 2`, two vertices and two edges between them (multi-edge) are added.
+///
+/// [Cycle graph]: https://en.wikipedia.org/wiki/Cycle_graph
+pub fn cycle<G: GraphTopologyAddition>(graph: &mut G, n: usize) -> (Vec<G::Vertex>, Vec<G::Edge>) {
+    graph.reserve_vertices(n);
+    graph.reserve_edges(n);
+    let vertices: Vec<_> = (0..n).map(|_| graph.add_vertex()).collect();
+    let edges = (0..n)
+        .map(|i| graph.add_edge(vertices[i], vertices[if i < n - 1 { i + 1 } else { 0 }]))
+        .collect();
+    (vertices, edges)
+}
+
+/// Generates a complete graph.
+///
+/// Generates a [complete graph] *K(n)* with `n` vertices and `n * (n - 1) / 2` edges in `graph` as
+/// a new connected component and returns the new vertices and edges.
+///
+/// For `n == 0`, nothing is added. For `n == 1`, only a single vertex is added.
+///
+/// [Complete graph]: https://en.wikipedia.org/wiki/Complete_graph
+pub fn complete<G: GraphTopologyAddition>(
+    graph: &mut G,
+    n: usize,
+) -> (Vec<G::Vertex>, Vec<G::Edge>) {
+    let edge_capacity = n * n.saturating_sub(1) / 2;
+    graph.reserve_vertices(n);
+    graph.reserve_edges(edge_capacity);
+    let vertices: Vec<_> = (0..n).map(|_| graph.add_vertex()).collect();
+    let mut edges = Vec::with_capacity(edge_capacity);
+    for (i, &u) in vertices.iter().enumerate() {
+        for &v in &vertices[i + 1..] {
+            edges.push(graph.add_edge(u, v));
+        }
+    }
+    (vertices, edges)
+}
 
 /// Generates a Petersen graph.
 ///
@@ -8,22 +121,15 @@ use crate::traits::{GraphTopology, GraphTopologyAddition};
 /// vertices and edges. This graph is also the Kneser graph *KG(5, 2)*.
 ///
 /// [Petersen graph]: https://en.wikipedia.org/wiki/Petersen_graph
-pub fn petersen<G>(
+pub fn petersen<G: GraphTopologyAddition>(graph: &mut G) -> (Vec<G::Vertex>, Vec<G::Edge>) {
-    graph: &mut G,
-) -> (
-    [<G as GraphTopology>::Vertex; 10],
-    [<G as GraphTopology>::Edge; 15],
-)
-where
-    G: GraphTopologyAddition,
-{
     const N: usize = 5;
     const K: usize = 2;
 
     graph.reserve_vertices(10);
     graph.reserve_edges(15);
-    let vertices = core::array::from_fn(|_| graph.add_vertex());
+    let vertices: Vec<_> = (0..10).map(|_| graph.add_vertex()).collect();
-    let edges = core::array::from_fn(|j| {
+    let edges = (0..15)
+        .map(|j| {
             let i = j / 3;
             match j % 3 {
                 0 => {
@@ -36,44 +142,449 @@ where
                 }
                 _ => graph.add_edge(vertices[i], vertices[i + N]),
             }
-    });
+        })
+        .collect();
     (vertices, edges)
 }
 
 #[cfg(test)]
 mod tests {
+    use std::fmt::Debug;
+
     use super::*;
-    use crate::models::AppendGraph;
+    use crate::testing::fixtures::MakeTestGraph;
+
+    #[derive(Debug, Clone, Copy)]
+    enum Spec {
+        Path(usize),
+        Cycle(usize),
+        Complete(usize),
+        Petersen,
+    }
+
+    impl Spec {
+        fn generate<G: GraphTopologyAddition>(
+            &self,
+            graph: &mut G,
+        ) -> (Vec<G::Vertex>, Vec<G::Edge>) {
+            match *self {
+                Spec::Path(n) => path(graph, n),
+                Spec::Cycle(n) => cycle(graph, n),
+                Spec::Complete(n) => complete(graph, n),
+                Spec::Petersen => petersen(graph),
+            }
+        }
+
+        fn assert<G: GraphTopology>(&self, built: &Built<G>)
+        where
+            G::Vertex: Debug,
+            G::Edge: Debug,
+        {
+            match *self {
+                Spec::Path(n) => assert_path(built, n),
+                Spec::Cycle(n) => assert_cycle(built, n),
+                Spec::Complete(n) => assert_complete(built, n),
+                Spec::Petersen => assert_petersen(built),
+            }
+        }
+    }
+
+    struct Built<G: GraphTopology> {
+        graph: G,
+        vertices: Vec<G::Vertex>,
+        edges: Vec<G::Edge>,
+        initial_vertex_count: usize,
+        initial_edge_count: usize,
+    }
+
+    /// Generates the test for the `append_graph` harness for the given `Spec` expression.
+    macro_rules! min_harness_tests {
+        ($spec:expr) => {
+            #[test]
+            fn append_graph() {
+                run($spec, add_to_empty::<$crate::models::AppendGraph>);
+            }
+        };
+    }
+
+    /// Generates one test per harness for the given `Spec` expression.
+    macro_rules! all_harness_tests {
+        ($spec:expr) => {
+            min_harness_tests!($spec);
 
             #[test]
-    fn petersen() {
+            fn append_graph_non_empty() {
-        let mut graph = AppendGraph::new();
+                run($spec, add_to_standard::<$crate::models::AppendGraph>);
-        let (vertices, edges) = super::petersen(&mut graph);
-        assert_eq!(
-            graph.vertex_count(),
-            10,
-            "unexpected number of added vertices"
-        );
-        assert_eq!(graph.edge_count(), 15, "unexpected number of added edges");
-        assert!(
-            graph.vertices().all(|v| graph.degree(v) == 3),
-            "all vertices should have degree 3"
-        );
-        assert_handles_in_graph(&graph, &vertices, &edges);
             }
 
-    fn assert_handles_in_graph<G: GraphTopology>(
+            #[test]
-        graph: &G,
+            fn graph() {
-        vertices: &[G::Vertex],
+                run($spec, add_to_empty::<$crate::models::Graph>);
-        edges: &[G::Edge],
+            }
+
+            #[test]
+            fn graph_non_empty() {
+                run($spec, add_to_standard::<$crate::models::Graph>);
+            }
+
+            #[test]
+            fn frozen_graph() {
+                run($spec, conv_generate_as::<$crate::models::FrozenGraph>);
+            }
+        };
+    }
+
+    /// Generates the module tree `<group>::<case>::<harness>` for each generator case.
+    ///
+    /// The `all_harnesses` cases run on every harness, the `min_harnesses` cases only on a reduced
+    /// set of harnesses.
+    macro_rules! generator_tests {
+        ($($group:ident {
+            all { $($all_case:ident => $all_generator:expr),+ $(,)? }
+            min { $($min_case:ident => $min_generator:expr),* $(,)? }
+        })+) => {
+            $(
+                mod $group {
+                    use super::*;
+
+                    $(
+                        mod $all_case {
+                            use super::*;
+
+                            all_harness_tests!($all_generator);
+                        }
+                    )+
+
+                    $(
+                        mod $min_case {
+                            use super::*;
+
+                            min_harness_tests!($min_generator);
+                        }
+                    )*
+                }
+            )+
+        };
+    }
+
+    generator_tests! {
+        path {
+            all {
+                small => Spec::Path(4),
+            }
+            min {
+                empty => Spec::Path(0),
+                single_vertex => Spec::Path(1),
+                single_edge => Spec::Path(2),
+                large => Spec::Path(21),
+            }
+        }
+        cycle {
+            all {
+                small_even => Spec::Cycle(4),
+            }
+            min {
+                empty => Spec::Cycle(0),
+                loop_edge => Spec::Cycle(1),
+                multi_edge => Spec::Cycle(2),
+                large_odd => Spec::Cycle(21),
+            }
+        }
+        complete {
+            all {
+                small_even => Spec::Complete(4),
+            }
+            min {
+                empty => Spec::Complete(0),
+                single_vertex => Spec::Complete(1),
+                single_edge => Spec::Complete(2),
+                large_odd => Spec::Complete(13),
+            }
+        }
+    }
+
+    mod petersen {
+        use super::*;
+
+        all_harness_tests!(Spec::Petersen);
+    }
+
+    /// Builds a graph with `harness` and asserts that it matches what `spec` should produce.
+    fn run<G: GraphTopology>(spec: Spec, harness: impl FnOnce(&Spec) -> Built<G>)
+    where
+        G::Vertex: Debug,
+        G::Edge: Debug,
+    {
+        let built = harness(&spec);
+        spec.assert(&built);
+    }
+
+    /// Runs `spec` on an empty graph of type `G`.
+    fn add_to_empty<G: GraphTopologyAddition>(spec: &Spec) -> Built<G> {
+        let mut graph = G::default();
+        let (vertices, edges) = spec.generate(&mut graph);
+        Built {
+            graph,
+            vertices,
+            edges,
+            initial_vertex_count: 0,
+            initial_edge_count: 0,
+        }
+    }
+
+    /// Runs `spec` on a non-empty test graph of type `G`.
+    fn add_to_standard<G: GraphTopologyAddition>(spec: &Spec) -> Built<G> {
+        let (mut graph, initial_vertices, initial_edges, _) = G::standard();
+        let (vertices, edges) = spec.generate(&mut graph);
+        Built {
+            graph,
+            vertices,
+            edges,
+            initial_vertex_count: initial_vertices.len(),
+            initial_edge_count: initial_edges.len(),
+        }
+    }
+
+    /// Runs `spec` within `generate_as` for type `G`.
+    fn conv_generate_as<G: GraphTopologyConversion>(spec: &Spec) -> Built<G> {
+        let (graph, vertices, edges) = generate_as::<G>(|graph| spec.generate(graph));
+        Built {
+            graph,
+            vertices,
+            edges,
+            initial_vertex_count: 0,
+            initial_edge_count: 0,
+        }
+    }
+
+    fn assert_path<G: GraphTopology>(built: &Built<G>, n: usize)
+    where
+        G::Vertex: Debug,
+        G::Edge: Debug,
+    {
+        assert_element_counts(built, n, n.saturating_sub(1));
+        assert_handles(built.graph.vertices(), &built.vertices, "vertex");
+        assert_handles(built.graph.edges(), &built.edges, "edge");
+        assert_no_loops(built);
+        assert_no_multi_edges(built);
+        match n {
+            0 => {}
+            1 => assert_eq!(
+                built.graph.degree(built.vertices[0]),
+                0,
+                "path n == 1 should be an isolated vertex"
+            ),
+            _ => {
+                for (i, &v) in built.vertices.iter().enumerate() {
+                    assert_eq!(
+                        built.graph.degree(v),
+                        if i == 0 || i == n - 1 { 1 } else { 2 },
+                        "unexpected degree of vertex {v:?} in path n == {n}"
+                    );
+                }
+            }
+        }
+        assert_path_order(built);
+    }
+
+    fn assert_cycle<G: GraphTopology>(built: &Built<G>, n: usize)
+    where
+        G::Vertex: Debug,
+        G::Edge: Debug,
+    {
+        assert_element_counts(built, n, n);
+        assert_handles(built.graph.vertices(), &built.vertices, "vertex");
+        assert_handles(built.graph.edges(), &built.edges, "edge");
+        if n != 1 {
+            assert_no_loops(built);
+        }
+        if n != 2 {
+            assert_no_multi_edges(built);
+        }
+        assert!(
+            built.vertices.iter().all(|&v| built.graph.degree(v) == 2),
+            "all new vertices should have degree 2"
+        );
+        assert_path_order(built);
+        // Asserts the closing edge e(n - 1) == (v(n - 1), v0).
+        if n > 0 {
+            // For n == 1, u == v and this validates the loop. For n == 2, the above asserted one of
+            // the two multi-edges, and this asserts the other.
+            let e = built.edges[n - 1];
+            let u = built.vertices[0];
+            let v = built.vertices[n - 1];
+            let incident_vertices = built.graph.incident_vertices(e);
+            assert!(
+                incident_vertices == (u, v) || incident_vertices == (v, u),
+                "edge {e:?} should have incident vertices {u:?} and {v:?}",
+            );
+        }
+    }
+
+    fn assert_complete<G: GraphTopology>(built: &Built<G>, n: usize)
+    where
+        G::Vertex: Debug,
+        G::Edge: Debug,
+    {
+        assert_element_counts(built, n, n * n.saturating_sub(1) / 2);
+        assert_handles(built.graph.vertices(), &built.vertices, "vertex");
+        assert_handles(built.graph.edges(), &built.edges, "edge");
+        // The predicate in `all` is only executed if `vertices` has any elements, i.e. for n > 0.
+        assert!(
+            built
+                .vertices
+                .iter()
+                .all(|&v| built.graph.degree(v) == n - 1),
+            "all new vertices should have degree {}",
+            n - 1
+        );
+        // Asserts that all pairs of vertices have exactly one edge between them. This also includes
+        // checks for loops and multi-edges. If there are no duplicates, then this implies that all
+        // expected edges were also matched due to the validated counts from above.
+        let mut seen = vec![false; n * n];
+        let position = |v, e| {
+            built
+                .vertices
+                .iter()
+                .position(|&x| x == v)
+                .unwrap_or_else(|| panic!("edge {e:?} has an invalid incident vertex {v:?}"))
+        };
+        for &e in &built.edges {
+            let (u, v) = built.graph.incident_vertices(e);
+            assert_ne!(u, v, "unexpected loop edge {e:?} at vertex {u:?}");
+            let (i, j) = (position(u, e), position(v, e));
+            let (i, j) = (i.min(j), i.max(j));
+            assert!(
+                !seen[i * n + j],
+                "unexpected multi-edge {e:?} between vertices {u:?} and {v:?}"
+            );
+            seen[i * n + j] = true;
+        }
+    }
+
+    fn assert_petersen<G: GraphTopology>(built: &Built<G>)
+    where
+        G::Vertex: Debug,
+        G::Edge: Debug,
+    {
+        assert_element_counts(built, 10, 15);
+        assert_handles(built.graph.vertices(), &built.vertices, "vertex");
+        assert_handles(built.graph.edges(), &built.edges, "edge");
+        assert_no_loops(built);
+        assert_no_multi_edges(built);
+        assert!(
+            built.vertices.iter().all(|&v| built.graph.degree(v) == 3),
+            "all new vertices should have degree 3"
+        );
+        // Checks that each pair of vertices (u, v) has no common neighbor if they are adjacent, and
+        // exactly one common neighbor otherwise.
+        for (i, &v) in built.vertices.iter().enumerate() {
+            for &u in &built.vertices[i + 1..] {
+                if built.graph.are_adjacent(v, u) {
+                    assert!(
+                        built.graph.common_neighbors(u, v).next().is_none(),
+                        "adjacent vertices {u:?} and {v:?} should not have a common neighbor"
+                    );
+                } else {
+                    assert_eq!(
+                        built.graph.common_neighbors(u, v).count(),
+                        1,
+                        "non-adjacent vertices {u:?} and {v:?} should have exactly one common neighbor"
+                    );
+                }
+            }
+        }
+    }
+
+    fn assert_element_counts<G: GraphTopology>(
+        built: &Built<G>,
+        expected_vertex_count: usize,
+        expected_edge_count: usize,
     ) {
-        assert!(
+        assert_eq!(
-            vertices.iter().all(|&v| graph.vertices().any(|u| u == v)),
+            built.graph.vertex_count(),
-            "all returned vertices should be in the graph"
+            built.initial_vertex_count + expected_vertex_count,
+            "unexpected number of added vertices"
         );
+        assert_eq!(
+            built.vertices.len(),
+            expected_vertex_count,
+            "unexpected number of returned vertices"
+        );
+        assert_eq!(
+            built.graph.edge_count(),
+            built.initial_edge_count + expected_edge_count,
+            "unexpected number of added edges"
+        );
+        assert_eq!(
+            built.edges.len(),
+            expected_edge_count,
+            "unexpected number of returned edges"
+        );
+    }
+
+    /// Asserts that every handle in `returned` is unique and in `all`.
+    fn assert_handles<T: PartialEq + Debug>(
+        all: impl Iterator<Item = T>,
+        returned: &[T],
+        kind: &str,
+    ) {
+        let mut remaining: Vec<T> = all.collect();
+        for e in returned {
+            let Some(position) = remaining.iter().position(|x| x == e) else {
+                panic!("returned {kind} {e:?} is not in the graph or appears more than once");
+            };
+            remaining.swap_remove(position);
+        }
+    }
+
+    fn assert_no_loops<G: GraphTopology>(built: &Built<G>)
+    where
+        G::Vertex: Debug,
+        G::Edge: Debug,
+    {
+        for &e in &built.edges {
+            let (u, v) = built.graph.incident_vertices(e);
+            assert_ne!(u, v, "unexpected loop edge {e:?} at vertex {u:?}");
+        }
+    }
+
+    fn assert_no_multi_edges<G: GraphTopology>(built: &Built<G>)
+    where
+        G::Vertex: Debug,
+    {
+        for &v in &built.vertices {
+            let mut neighbors = Vec::new();
+            let mut loop_count = 0;
+            for u in built.graph.adjacent_vertices(v) {
+                if u == v {
+                    loop_count += 1;
+                    assert!(loop_count < 3, "unexpected multi-edge loop at vertex {v:?}");
+                } else {
                     assert!(
-            edges.iter().all(|&e| graph.edges().any(|f| f == e)),
+                        !neighbors.contains(&u),
-            "all returned edges should be in the graph"
+                        "unexpected multi-edge between vertices {v:?} and {u:?}"
+                    );
+                    neighbors.push(u);
+                }
+            }
+        }
+    }
+
+    /// Asserts that each returned edge *ei* connects the returned vertices *vi* and *v(i + 1)*.
+    fn assert_path_order<G: GraphTopology>(built: &Built<G>)
+    where
+        G::Vertex: Debug,
+        G::Edge: Debug,
+    {
+        for (w, &e) in built.vertices.windows(2).zip(&built.edges) {
+            let incident_vertices = built.graph.incident_vertices(e);
+            assert!(
+                incident_vertices == (w[0], w[1]) || incident_vertices == (w[1], w[0]),
+                "edge {e:?} should have incident vertices {:?} and {:?}",
+                w[0],
+                w[1]
             );
         }
     }
+}

src/maps.rs

@@ -141,9 +141,10 @@ impl<E: Copy, T: Clone> IndexMut<E> for ElementMap<E, T> {
 
 #[cfg(test)]
 mod tests {
-    use super::*;
     use std::rc::Rc;
 
+    use super::*;
+
     #[test]
     fn initial_values_are_default() {
         let map = ElementMap::new(42, |e| e, 6);

src/testing/fixtures.rs

@@ -5,6 +5,7 @@ use crate::models::{AppendGraph, FrozenGraph};
 use crate::traits::{GraphTopology, GraphTopologyAddition, GraphTopologyConversion, Incidence};
 
 pub trait MakeTestGraph: GraphTopology + Sized {
+    /// Returns a versatile, pre-defined standard test graph.
     // Since this is only a test fixture, the complex return type here is deemed acceptable.
     #[allow(clippy::type_complexity)]
     fn standard() -> (
@@ -14,20 +15,32 @@ pub trait MakeTestGraph: GraphTopology + Sized {
         [Vec<Incidence<Self::Vertex, Self::Edge>>; 10],
     );
 
+    /// Returns an empty graph.
     fn empty() -> Self;
 
+    /// Returns a graph with a single vertex and no edges.
     fn single_vertex() -> (Self, Self::Vertex);
 
+    /// Returns a graph with two vertices connected by a single edge.
     fn single_edge() -> (Self, [Self::Vertex; 2], Self::Edge);
 
+    /// Returns a graph with vertices *v0*, *v1*, and *v2*, where *v0* is isolated, and the other
+    /// two are connected by a single edge.
     fn disconnected() -> (Self, [Self::Vertex; 3]);
 
+    /// Returns a graph with a single vertex that has a single loop edge.
     fn loop_edge() -> (Self, Self::Vertex, Self::Edge);
 
+    /// Returns a graph with two vertices that are connected by `K` multi-edges.
     fn multiple_edges<const K: usize>() -> (Self, [Self::Vertex; 2], [Self::Edge; K]);
 
+    /// Returns a graph that is a path with three vertices and two edges between them, returned in
+    /// order.
     fn two_edge_path() -> (Self, [Self::Vertex; 3], [Self::Edge; 2]);
 
+    /// Returns a graph that is a path with three vertices *v0*, *v1*, and *v2*, and two edges
+    /// *e0 = (v0, v1)* and *e1 = (v1, v2)* between them, and two loops on the first two vertices
+    /// *e2 = (v0, v0)* and *e3 = (v1, v1)*.
     fn two_edge_path_with_loops() -> (Self, [Self::Vertex; 3], [Self::Edge; 4]);
 }
 
@@ -268,13 +281,12 @@ where
     F: Fn(V) -> Option<u32>,
 {
     let expected = [0, 1, 2, 2, 2, 3, 3, 3, 3, 4];
-    for (i, v) in vertices.iter().enumerate() {
+    for (i, &v) in vertices.iter().enumerate() {
         assert_eq!(
-            actual_for(*v),
+            actual_for(v),
             Some(expected[i]),
-            "unexpected distance from vertex {:?} to vertex {:?}",
+            "unexpected distance from vertex {:?} to vertex {v:?}",
-            vertices[0],
+            vertices[0]
-            vertices[i]
         );
     }
 }
@@ -308,8 +320,8 @@ pub fn assert_standard_unweighted_predecessors_v0<V: Debug + Copy + PartialEq>(
 /// Asserts that the path given as `path_option` is a valid path in `graph`
 ///
 /// Walks the path and asserts that it is `Some`, that it is empty if and only if
-/// `source == target`, that its edges are pairwise incident in the order given, and that it starts
+/// `source == target` for any `target` in `targets`, that its edges are pairwise incident in the
-/// at `source` and ends at `target`.
+/// order given, and that it starts at `source` and ends at any `target` in `targets`.
 pub fn assert_valid_path<G: GraphTopology>(
     graph: &G,
     path_option: Option<Vec<G::Edge>>,

src/testing/graph_topology_testing.rs

@@ -49,6 +49,12 @@ macro_rules! graph_topology_tests {
             incidence_cursor_copy,
             incident_vertices_incidences_consistency,
             incident_edges_incidences_consistency,
+            common_neighbors,
+            common_neighbors_same_vertex,
+            common_neighbors_single,
+            common_neighbors_disconnected,
+            common_neighbors_multiple_edges,
+            common_neighbors_loop_edge,
         );
     };
 
@@ -771,3 +777,118 @@ where
         );
     }
 }
+
+pub fn common_neighbors<G: MakeTestGraph>()
+where
+    G::Vertex: Debug,
+{
+    let (graph, vertices, _, _) = G::standard();
+    // Pairs of vertex indices with the indices of their expected common neighbors.
+    let cases: [(usize, usize, &[usize]); _] = [
+        (0, 3, &[1]),
+        (1, 6, &[2, 3]),
+        (5, 8, &[]),
+        (2, 9, &[5, 6]),
+        (7, 3, &[]),
+        (0, 1, &[]),
+        (6, 7, &[9]),
+        // Loop only on one side, adjacent.
+        (2, 6, &[2]),
+        // Loop only on one side, not adjacent.
+        (2, 7, &[4]),
+        // Adjacent through a double edge, and both have a loop.
+        (2, 4, &[1, 2, 4]),
+    ];
+    for (i, j, expected) in cases {
+        let expected: Vec<_> = expected.iter().map(|&k| vertices[k]).collect();
+        assert_common_neighbors(&graph, vertices[i], vertices[j], &expected);
+    }
+}
+
+pub fn common_neighbors_same_vertex<G: MakeTestGraph>()
+where
+    G::Vertex: Debug,
+{
+    let (graph, vertices, _, _) = G::standard();
+    // Vertex 1 has a double edge to vertex 0, but no loop.
+    assert_common_neighbors(
+        &graph,
+        vertices[1],
+        vertices[1],
+        &[vertices[0], vertices[2], vertices[3], vertices[4]],
+    );
+    // Vertex 4 has a loop, and is therefore its own common neighbor with itself.
+    assert_common_neighbors(
+        &graph,
+        vertices[4],
+        vertices[4],
+        &[
+            vertices[1],
+            vertices[2],
+            vertices[4],
+            vertices[7],
+            vertices[8],
+        ],
+    );
+}
+
+pub fn common_neighbors_single<G: MakeTestGraph>()
+where
+    G::Vertex: Debug,
+{
+    let (graph, v) = G::single_vertex();
+    assert_common_neighbors(&graph, v, v, &[]);
+}
+
+pub fn common_neighbors_disconnected<G: MakeTestGraph>()
+where
+    G::Vertex: Debug,
+{
+    let (graph, v) = G::disconnected();
+    assert_common_neighbors(&graph, v[0], v[0], &[]);
+    assert_common_neighbors(&graph, v[0], v[1], &[]);
+}
+
+pub fn common_neighbors_multiple_edges<G: MakeTestGraph>()
+where
+    G::Vertex: Debug,
+{
+    let (graph, [v0, v1], _) = G::multiple_edges::<3>();
+    assert_common_neighbors(&graph, v0, v1, &[]);
+    assert_common_neighbors(&graph, v1, v1, &[v0]);
+}
+
+pub fn common_neighbors_loop_edge<G: MakeTestGraph>()
+where
+    G::Vertex: Debug,
+{
+    let (graph, v, _) = G::loop_edge();
+    assert_common_neighbors(&graph, v, v, &[v]);
+}
+
+/// Asserts that `u` and `v` have exactly the `expected` common neighbors, each yielded once, for
+/// both argument orders.
+fn assert_common_neighbors<G: MakeTestGraph>(
+    graph: &G,
+    u: G::Vertex,
+    v: G::Vertex,
+    expected: &[G::Vertex],
+) where
+    G::Vertex: Debug,
+{
+    for (a, b) in [(u, v), (v, u)] {
+        let mut remaining = expected.to_vec();
+        for w in graph.common_neighbors(a, b) {
+            let pos = remaining.iter().position(|&x| x == w).unwrap_or_else(|| {
+                panic!(
+                    "unexpected or repeated common neighbor {w:?} of vertices {a:?} and {b:?} from iterator"
+                )
+            });
+            remaining.swap_remove(pos);
+        }
+        assert!(
+            remaining.is_empty(),
+            "expected common neighbors {remaining:?} of vertices {a:?} and {b:?} were not matched by iterator"
+        );
+    }
+}

src/traits.rs

@@ -175,6 +175,58 @@ pub trait GraphTopology {
     ///
     /// Panics if `v` is not a valid vertex of this graph.
     fn incidence_cursor(&self, v: Self::Vertex) -> Self::IncidenceCursor;
+
+    /// Returns an iterator over all vertices that are adjacent to both `u` and `v`.
+    ///
+    /// Every common neighbor is yielded exactly once, in unspecified order, regardless of how
+    /// many parallel edges connect it to `u` or `v`. This method is symmetric up to permutations,
+    /// i.e. swapping the arguments will yield the same vertices, but not necessarily in the same
+    /// order.
+    ///
+    /// If `u` has a loop and is adjacent to `v`, then `u` is a common neighbor, and will be yielded
+    /// exactly once, and analogously for a loop at `v`.
+    ///
+    /// If `u == v`, then the common neighbors are all neighbors of `u`, including `u` itself if and
+    /// only if it has a loop.
+    ///
+    /// All neighbors of `u` are collected when this method is called, while those of `v` are
+    /// traversed lazily.
+    ///
+    /// # Panics
+    ///
+    /// Panics if `u` or `v` is not a valid vertex of this graph.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use grapherity::models::AppendGraph;
+    /// use grapherity::prelude::*;
+    ///
+    /// let mut graph = AppendGraph::new();
+    /// let [u, w, v] = core::array::from_fn(|_| graph.add_vertex());
+    /// // Parallel edges do not yield `w` more than once.
+    /// graph.add_edge(u, w);
+    /// graph.add_edge(u, w);
+    /// graph.add_edge(w, v);
+    /// assert!(graph.common_neighbors(u, v).eq([w]));
+    /// ```
+    // TODO: FrozenGraph could provide a sorted-merge override, if its vertices were sorted.
+    fn common_neighbors(
+        &self,
+        u: Self::Vertex,
+        v: Self::Vertex,
+    ) -> impl Iterator<Item = Self::Vertex> {
+        // TODO: Instead of Vec, this could use a vertex ElementMap with marked neighbors if the product of the degrees of u and v is large compared to |V|.
+        // TODO: Instead of Vec, this could use a reusable, user-provided(?) "scratch-pad" vertex ElementMap, to not pay its allocation.
+        let mut u_neighbors: Vec<_> = self.adjacent_vertices(u).collect();
+        let mut v_neighbors = self.adjacent_vertices(v);
+        std::iter::from_fn(move || {
+            let w = v_neighbors.find(|w| u_neighbors.contains(w))?;
+            // Removes all parallel entries, so that `w` is not yielded again.
+            u_neighbors.retain(|x| *x != w);
+            Some(w)
+        })
+    }
 }
 
 /// A trait that adds construction operations to an undirected graph topology.