src/models/append_graph.rs

@@ -120,6 +120,12 @@ impl GraphTopology for AppendGraph {
         .map(|(v, _)| v)
     }
 
+    fn incident_vertices(&self, e: Self::Edge) -> (Self::Vertex, Self::Vertex) {
+        let v2 = self.incidences[e.0].adjacent;
+        let v1 = self.incidences[e.0 ^ 1].adjacent;
+        (v1, v2)
+    }
+
     fn edges(&self) -> impl Iterator<Item = Self::Edge> {
         (0..self.incidences.len()).step_by(2).map(Incidence)
     }
@@ -153,4 +159,18 @@ mod tests {
 
     crate::graph_topology_test_fixtures!(AppendGraph);
     crate::graph_topology_tests!(AppendGraph);
+
+    #[test]
+    fn incident_vertices_paired_index() {
+        let mut graph = AppendGraph::new();
+        let v1 = graph.add_vertex();
+        let v2 = graph.add_vertex();
+        let e = graph.add_edge(v1, v2);
+        let f = Incidence(e.0 + 1);
+        let (u1, u2) = graph.incident_vertices(f);
+        assert!(
+            (u1 == v1 && u2 == v2) || (u1 == v2 && u2 == v1),
+            "unexpected incident vertices {u1:?} and {u2:?} for edge {f:?}"
+        );
+    }
 }

src/models/graph.rs

@@ -176,6 +176,19 @@ impl GraphTopology for Graph {
             .map(|(vs, _)| self.vertices.get_idx(vs.0).unwrap())
     }
 
+    fn incident_vertices(&self, e: Self::Edge) -> (Self::Vertex, Self::Vertex) {
+        let v2 = self
+            .vertices
+            .get_idx(self.incidences[e].adjacent.0)
+            .unwrap();
+        let f = self.incidences.get_idx(e.arr_idx() ^ 1).unwrap();
+        let v1 = self
+            .vertices
+            .get_idx(self.incidences[f].adjacent.0)
+            .unwrap();
+        (v1, v2)
+    }
+
     fn edges(&self) -> impl Iterator<Item = Self::Edge> {
         self.incidences
             .iter()
@@ -249,6 +262,23 @@ mod tests {
     crate::graph_topology_tests!(Graph);
     crate::graph_topology_deletion_tests!(Graph);
 
+    #[test]
+    fn incident_vertices_paired_index() {
+        let mut graph = Graph::new();
+        let v1 = graph.add_vertex();
+        let v2 = graph.add_vertex();
+        let e = graph.add_edge(v1, v2);
+        let f = graph
+            .incidences
+            .get_idx(e.arr_idx() + 1)
+            .expect("paired index should be valid");
+        let (u1, u2) = graph.incident_vertices(f);
+        assert!(
+            (u1 == v1 && u2 == v2) || (u1 == v2 && u2 == v1),
+            "unexpected incident vertices {u1:?} and {u2:?} for edge {f:?}"
+        );
+    }
+
     #[test]
     fn delete_edge_paired_index() {
         let mut graph = Graph::new();

src/testing/graph_topology_testing.rs

@@ -365,6 +365,84 @@ macro_rules! graph_topology_tests {
             }
         }
 
+        #[test]
+        fn incident_vertices_single_edge() {
+            let mut graph = <$T>::new();
+            let v1 = graph.add_vertex();
+            let v2 = graph.add_vertex();
+            let e = graph.add_edge(v1, v2);
+            let (u1, u2) = graph.incident_vertices(e);
+            assert!(
+                (u1 == v1 && u2 == v2) || (u1 == v2 && u2 == v1),
+                "unexpected incident vertices {u1:?} and {u2:?} for edge {e:?}"
+            );
+        }
+
+        #[test]
+        fn incident_vertices_loop_edge() {
+            let mut graph = <$T>::new();
+            let v = graph.add_vertex();
+            let e = graph.add_edge(v, v);
+            assert_eq!(
+                graph.incident_vertices(e),
+                (v, v),
+                "unexpected incident vertices for loop edge {e:?}"
+            );
+        }
+
+        #[test]
+        fn incident_vertices_multiple_edges() {
+            let mut graph = <$T>::new();
+            let v1 = graph.add_vertex();
+            let v2 = graph.add_vertex();
+            let e1 = graph.add_edge(v1, v2);
+            let e2 = graph.add_edge(v1, v2);
+            assert_ne!(e1, e2, "edges should be distinct");
+            let (u1, u2) = graph.incident_vertices(e1);
+            assert!(
+                (u1 == v1 && u2 == v2) || (u1 == v2 && u2 == v1),
+                "unexpected incident vertices {u1:?} and {u2:?} for first multi-edge {e1:?}"
+            );
+            let (u1, u2) = graph.incident_vertices(e2);
+            assert!(
+                (u1 == v1 && u2 == v2) || (u1 == v2 && u2 == v1),
+                "unexpected incident vertices {u1:?} and {u2:?} for second multi-edge {e2:?}"
+            );
+        }
+
+        #[test]
+        fn incident_vertices() {
+            let (graph, vertices, edges, _) = make_test_graph();
+            let expected: [(<$T as $crate::traits::GraphTopology>::Vertex, <$T as $crate::traits::GraphTopology>::Vertex); 18] = [
+                (vertices[0], vertices[1]),
+                (vertices[0], vertices[1]),
+                (vertices[1], vertices[2]),
+                (vertices[1], vertices[3]),
+                (vertices[1], vertices[4]),
+                (vertices[2], vertices[2]),
+                (vertices[2], vertices[4]),
+                (vertices[2], vertices[4]),
+                (vertices[2], vertices[5]),
+                (vertices[2], vertices[6]),
+                (vertices[3], vertices[6]),
+                (vertices[4], vertices[4]),
+                (vertices[4], vertices[7]),
+                (vertices[4], vertices[8]),
+                (vertices[5], vertices[9]),
+                (vertices[6], vertices[9]),
+                (vertices[7], vertices[8]),
+                (vertices[7], vertices[9]),
+            ];
+            for (i, &(v1, v2)) in expected.iter().enumerate() {
+                let (u1, u2) = graph.incident_vertices(edges[i]);
+                assert!(
+                    (u1 == v1 && u2 == v2) || (u1 == v2 && u2 == v1),
+                    "unexpected incident vertices {u1:?} and {u2:?} for edges[{i}]: edge {:?}",
+                    edges[i]
+                );
+            }
+        }
+
         #[test]
         fn edges_empty() {
             let graph = <$T>::new();
@@ -514,6 +592,20 @@ macro_rules! graph_topology_tests {
                     vertices[i]
                 );
             }
+        }
+
+               #[test]
+        fn incident_vertices_incidences_consistency() {
+            let (graph, _, _, _) = make_test_graph();
+            for u in graph.vertices() {
+                for (v, e) in graph.incidences(u) {
+                    let (w1, w2) = graph.incident_vertices(e);
+                    assert!(
+                        (w1 == u && w2 == v) || (w1 == v && w2 == u),
+                        "incident vertices {w1:?} and {w2:?} of edge {e:?} are inconsistent with incidence ({v:?}, {e:?}) of vertex {u:?}"
+                    );
+                }
+            }
         }
     };
 }
@@ -800,6 +892,43 @@ macro_rules! graph_topology_deletion_tests {
             }
         }
 
+        #[test]
+        fn incident_vertices_after_delete_edge() {
+            let (mut graph, vertices, edges, _) = make_test_graph();
+            graph.delete_edge(edges[2]);
+            let expected: [(
+                usize,
+                <Graph as $crate::traits::GraphTopology>::Vertex,
+                <Graph as $crate::traits::GraphTopology>::Vertex,
+            ); 17] = [
+                (0, vertices[0], vertices[1]),
+                (1, vertices[0], vertices[1]),
+                (3, vertices[1], vertices[3]),
+                (4, vertices[1], vertices[4]),
+                (5, vertices[2], vertices[2]),
+                (6, vertices[2], vertices[4]),
+                (7, vertices[2], vertices[4]),
+                (8, vertices[2], vertices[5]),
+                (9, vertices[2], vertices[6]),
+                (10, vertices[3], vertices[6]),
+                (11, vertices[4], vertices[4]),
+                (12, vertices[4], vertices[7]),
+                (13, vertices[4], vertices[8]),
+                (14, vertices[5], vertices[9]),
+                (15, vertices[6], vertices[9]),
+                (16, vertices[7], vertices[8]),
+                (17, vertices[7], vertices[9]),
+            ];
+            for (i, v1, v2) in expected {
+                let (u1, u2) = graph.incident_vertices(edges[i]);
+                assert!(
+                    (u1 == v1 && u2 == v2) || (u1 == v2 && u2 == v1),
+                    "unexpected incident vertices {u1:?} and {u2:?} for edges[{i}] ({:?}) after delete",
+                    edges[i]
+                );
+            }
+        }
+
         #[test]
         fn edges_after_delete() {
             let (mut graph, vertices, edges, _) = make_test_graph();

src/traits.rs

@@ -2,7 +2,6 @@ use crate::maps::{EdgeMap, VertexMap};
 
 // TODO: Add functions to reserve memory for vertices and edges.
 // TODO: Add iterator of incident edges for a vertex.
-// TODO: Add finding incident vertices for an edge.
 // TODO: Split out GraphTopologyAddition trait.
 pub trait GraphTopology {
     type Vertex: Copy + Eq;
@@ -18,6 +17,7 @@ pub trait GraphTopology {
     fn are_adjacent(&self, v1: Self::Vertex, v2: Self::Vertex) -> bool;
     fn vertices(&self) -> impl Iterator<Item = Self::Vertex>;
     fn adjacent_vertices(&self, v: Self::Vertex) -> impl Iterator<Item = Self::Vertex>;
+    fn incident_vertices(&self, e: Self::Edge) -> (Self::Vertex, Self::Vertex);
     fn edges(&self) -> impl Iterator<Item = Self::Edge>;
     fn incidences(&self, v: Self::Vertex) -> impl Iterator<Item = (Self::Vertex, Self::Edge)>;
     fn add_vertex(&mut self) -> Self::Vertex;