src/models/append_graph.rs

@@ -7,6 +7,12 @@ pub struct Vertex(usize);
 #[derive(Copy, Clone, PartialEq, Eq, Debug)]
 pub struct Incidence(usize);
 
+impl Incidence {
+    fn normalize(&self) -> Self {
+        Self(self.0 & !1)
+    }
+}
+
 struct VertexIncidenceHeader {
     incidence_count: usize,
     first_incidence: Option<Incidence>,
@@ -26,13 +32,29 @@ impl<'a> Iterator for AdjacentVertexIterator<'a> {
     type Item = Vertex;
 
     fn next(&mut self) -> Option<Self::Item> {
-        let incidence = self.incidence?;
-        let entry = &self.graph.incidences[incidence.0];
+        let current = self.incidence?;
+        let entry = &self.graph.incidences[current.0];
         self.incidence = entry.next;
         Some(entry.adjacent)
     }
 }
 
+struct IncidenceIterator<'a> {
+    graph: &'a AppendGraph,
+    incidence: Option<Incidence>,
+}
+
+impl<'a> Iterator for IncidenceIterator<'a> {
+    type Item = (Vertex, Incidence);
+
+    fn next(&mut self) -> Option<Self::Item> {
+        let current = self.incidence?;
+        let entry = &self.graph.incidences[current.0];
+        self.incidence = entry.next;
+        Some((entry.adjacent, current.normalize()))
+    }
+}
+
 pub struct AppendGraph {
     // TODO: Index 'vertices' by a 'Vertex' instead of 'Vertex.0'?
     vertices: Vec<VertexIncidenceHeader>,
@@ -117,6 +139,13 @@ impl GraphTopology for AppendGraph {
         (0..self.incidences.len()).step_by(2).map(Incidence)
     }
 
+    fn incidences(&self, v: Self::Vertex) -> impl Iterator<Item = (Self::Vertex, Self::Edge)> {
+        IncidenceIterator {
+            graph: self,
+            incidence: self.vertices[v.0].first_incidence,
+        }
+    }
+
     fn add_vertex(&mut self) -> Self::Vertex {
         self.vertices.push(VertexIncidenceHeader {
             incidence_count: 0,

src/models/graph.rs

@@ -70,6 +70,24 @@ impl IncidentEdgeCursor {
     }
 }
 
+struct IncidenceIterator<'a> {
+    graph: &'a Graph,
+    incidence: Option<IncidenceSlot>,
+}
+
+impl<'a> Iterator for IncidenceIterator<'a> {
+    type Item = (Vertex, Edge);
+
+    fn next(&mut self) -> Option<Self::Item> {
+        let current = self.incidence?;
+        let e = self.graph.incidences.get_idx(current.0).unwrap();
+        let entry = &self.graph.incidences[e];
+        self.incidence = entry.next;
+        let v = self.graph.vertices.get_idx(entry.adjacent.0).unwrap();
+        Some((v, self.graph.normalize_edge(e)))
+    }
+}
+
 pub struct Graph {
     // TODO: Arena index and generation types could be externalized to Graph.
     vertices: Arena<VertexIncidenceHeader, usize, usize>,
@@ -142,6 +160,10 @@ impl Graph {
             self.incidences[previous].next = next;
         }
     }
+
+    fn normalize_edge(&self, e: Edge) -> Edge {
+        self.incidences.get_idx(e.arr_idx() & !1).unwrap()
+    }
 }
 
 impl Default for Graph {
@@ -205,6 +227,13 @@ impl GraphTopology for Graph {
             .map(|(i, _)| i)
     }
 
+    fn incidences(&self, v: Self::Vertex) -> impl Iterator<Item = (Self::Vertex, Self::Edge)> {
+        IncidenceIterator {
+            graph: self,
+            incidence: self.vertices[v].first_incidence,
+        }
+    }
+
     fn add_vertex(&mut self) -> Self::Vertex {
         self.vertices.insert(VertexIncidenceHeader {
             incidence_count: 0,

src/testing/graph_topology_testing.rs

@@ -6,6 +6,10 @@ macro_rules! graph_topology_test_fixtures {
             $T,
             [<$T as $crate::traits::GraphTopology>::Vertex; 10],
             [<$T as $crate::traits::GraphTopology>::Edge; 18],
+            [Vec<(
+                <$T as $crate::traits::GraphTopology>::Vertex,
+                <$T as $crate::traits::GraphTopology>::Edge,
+            )>; 10],
         ) {
             let mut graph = <$T>::new();
             let vertices: [<$T as $crate::traits::GraphTopology>::Vertex; 10] =
@@ -30,7 +34,53 @@ macro_rules! graph_topology_test_fixtures {
                 graph.add_edge(vertices[7], vertices[8]),
                 graph.add_edge(vertices[7], vertices[9]),
             ];
-            (graph, vertices, edges)
+            let incidences: [Vec<_>; 10] = [
+                vec![(vertices[1], edges[0]), (vertices[1], edges[1])],
+                vec![
+                    (vertices[0], edges[0]),
+                    (vertices[0], edges[1]),
+                    (vertices[2], edges[2]),
+                    (vertices[3], edges[3]),
+                    (vertices[4], edges[4]),
+                ],
+                vec![
+                    (vertices[2], edges[5]),
+                    (vertices[2], edges[5]),
+                    (vertices[1], edges[2]),
+                    (vertices[4], edges[6]),
+                    (vertices[4], edges[7]),
+                    (vertices[5], edges[8]),
+                    (vertices[6], edges[9]),
+                ],
+                vec![(vertices[1], edges[3]), (vertices[6], edges[10])],
+                vec![
+                    (vertices[1], edges[4]),
+                    (vertices[2], edges[6]),
+                    (vertices[2], edges[7]),
+                    (vertices[4], edges[11]),
+                    (vertices[4], edges[11]),
+                    (vertices[7], edges[12]),
+                    (vertices[8], edges[13]),
+                ],
+                vec![(vertices[2], edges[8]), (vertices[9], edges[14])],
+                vec![
+                    (vertices[2], edges[9]),
+                    (vertices[3], edges[10]),
+                    (vertices[9], edges[15]),
+                ],
+                vec![
+                    (vertices[4], edges[12]),
+                    (vertices[8], edges[16]),
+                    (vertices[9], edges[17]),
+                ],
+                vec![(vertices[4], edges[13]), (vertices[7], edges[16])],
+                vec![
+                    (vertices[5], edges[14]),
+                    (vertices[6], edges[15]),
+                    (vertices[7], edges[17]),
+                ],
+            ];
+            (graph, vertices, edges, incidences)
         }
     };
 }
@@ -54,7 +104,7 @@ macro_rules! graph_topology_tests {
 
         #[test]
         fn vertex_count() {
-            let (graph, _, _) = make_test_graph();
+            let (graph, _, _, _) = make_test_graph();
             assert_eq!(graph.vertex_count(), 10, "unexpected vertex count");
         }
 
@@ -75,7 +125,7 @@ macro_rules! graph_topology_tests {
 
         #[test]
         fn edge_count() {
-            let (graph, _, _) = make_test_graph();
+            let (graph, _, _, _) = make_test_graph();
             assert_eq!(graph.edge_count(), 18, "unexpected edge count");
         }
 
@@ -88,7 +138,7 @@ macro_rules! graph_topology_tests {
 
         #[test]
         fn degree() {
-            let (graph, vertices, _) = make_test_graph();
+            let (graph, vertices, _, _) = make_test_graph();
             let expected_degrees = [2, 5, 7, 2, 7, 2, 3, 3, 2, 3];
             for i in 0..graph.vertex_count() {
                 assert_eq!(
@@ -100,6 +150,36 @@ macro_rules! graph_topology_tests {
             }
         }
 
+        #[test]
+        fn loop_edge() {
+            let mut graph = <$T>::new();
+            let v = graph.add_vertex();
+            graph.add_edge(v, v);
+            assert_eq!(graph.vertex_count(), 1, "unexpected vertex count");
+            assert_eq!(graph.edge_count(), 1, "unexpected edge count");
+            assert_eq!(graph.degree(v), 2, "unexpected degree");
+            assert!(
+                graph.are_adjacent(v, v),
+                "vertex with loop edge should be adjacent to itself"
+            );
+        }
+
+        #[test]
+        fn multiple_edges() {
+            let k = 3;
+            let mut graph = <$T>::new();
+            let v1 = graph.add_vertex();
+            let v2 = graph.add_vertex();
+            for _ in 0..k {
+                graph.add_edge(v1, v2);
+            }
+            assert_eq!(graph.vertex_count(), 2, "unexpected vertex count");
+            assert_eq!(graph.edge_count(), k, "unexpected edge count");
+            assert_eq!(graph.degree(v1), k, "unexpected degree of vertex {v1:?}");
+            assert_eq!(graph.degree(v2), k, "unexpected degree of vertex {v2:?}");
+            assert!(graph.are_adjacent(v1, v2), "should be adjacent");
+        }
+
         #[test]
         fn are_adjacent_vertex_self() {
             let mut graph = <$T>::new();
@@ -124,7 +204,7 @@ macro_rules! graph_topology_tests {
 
         #[test]
         fn are_adjacent() {
-            let (graph, vertices, _) = make_test_graph();
+            let (graph, vertices, _, _) = make_test_graph();
             assert!(
                 graph.are_adjacent(vertices[0], vertices[1]),
                 "expected {:?} and {:?} to be adjacent",
@@ -178,7 +258,7 @@ macro_rules! graph_topology_tests {
 
         #[test]
         fn vertices() {
-            let (graph, vertices, _) = make_test_graph();
+            let (graph, vertices, _, _) = make_test_graph();
             assert_eq!(graph.vertices().count(), 10, "unexpected vertex count");
 
             // Expects each vertex to appear exactly once.
@@ -194,9 +274,9 @@ macro_rules! graph_topology_tests {
         #[test]
         fn adjacent_vertices_empty() {
             let mut graph = <$T>::new();
-            let vertex = graph.add_vertex();
+            let v = graph.add_vertex();
             assert_eq!(
-                graph.adjacent_vertices(vertex).count(),
+                graph.adjacent_vertices(v).count(),
                 0,
                 "adjacent vertex iterator of vertex with degree 0 should have no elements"
             );
@@ -204,7 +284,7 @@ macro_rules! graph_topology_tests {
 
         #[test]
         fn adjacent_vertices() {
-            let (graph, vertices, _) = make_test_graph();
+            let (graph, vertices, _, _) = make_test_graph();
             // Checks adjacency of vertex 4.
             assert_eq!(
                 graph.adjacent_vertices(vertices[4]).count(),
@@ -240,42 +320,10 @@ macro_rules! graph_topology_tests {
         }
 
         #[test]
-        fn edges_empty() {
-            let graph = <$T>::new();
-            assert_eq!(
-                graph.edges().count(),
-                0,
-                "edge iterator of empty graph should have no elements"
-            );
-        }
-
-        #[test]
-        fn edges() {
-            let (graph, _, edges) = make_test_graph();
-            assert_eq!(graph.edges().count(), 18, "unexpected edge count");
-
-            // Expects each edge to appear exactly once.
-            for e in graph.edges() {
-                assert_eq!(
-                    edges.iter().filter(|&x| *x == e).count(),
-                    1,
-                    "unexpected edge {e:?} from the iterator"
-                );
-            }
-        }
-
-        #[test]
-        fn loop_edge() {
+        fn adjacent_vertices_loop_edge() {
             let mut graph = <$T>::new();
             let v = graph.add_vertex();
             graph.add_edge(v, v);
-            assert_eq!(graph.vertex_count(), 1, "unexpected vertex count");
-            assert_eq!(graph.edge_count(), 1, "unexpected edge count");
-            assert_eq!(graph.degree(v), 2, "unexpected degree");
-            assert!(
-                graph.are_adjacent(v, v),
-                "vertex with loop edge should be adjacent to itself"
-            );
             let mut iter = graph.adjacent_vertices(v);
             assert_eq!(iter.next(), Some(v), "vertex should be adjacent to itself");
             assert_eq!(
@@ -291,35 +339,172 @@ macro_rules! graph_topology_tests {
         }
 
         #[test]
-        fn multiple_edges() {
+        fn adjacent_vertices_multiple_edges() {
             let k = 3;
             let mut graph = <$T>::new();
             let vertices = [graph.add_vertex(), graph.add_vertex()];
             for _ in 0..k {
                 graph.add_edge(vertices[0], vertices[1]);
             }
-            assert_eq!(
-                graph.vertex_count(),
-                vertices.len(),
-                "unexpected vertex count"
-            );
-            assert_eq!(graph.edge_count(), k, "unexpected edge count");
-            for v in vertices {
-                assert_eq!(graph.degree(v), k, "unexpected degree of {v:?}");
-            }
-            assert!(
-                graph.are_adjacent(vertices[0], vertices[1]),
-                "should be adjacent"
-            );
             for i in 0..2 {
                 let mut iter = graph.adjacent_vertices(vertices[i]);
                 for j in 0..k {
                     assert_eq!(
                         iter.next(),
                         Some(vertices[1 - i]),
-                        "adjacent vertex {j} of vertex {:?} should be {:?}",
+                        "unexpected adjacent vertex {j} of vertex {:?}",
+                        vertices[i]
+                    );
+                }
+                assert_eq!(
+                    iter.next(),
+                    None,
+                    "too many adjacent vertices of vertex {:?} from iterator",
+                    vertices[i]
+                );
+            }
+        }
+
+        #[test]
+        fn edges_empty() {
+            let graph = <$T>::new();
+            assert_eq!(
+                graph.edges().count(),
+                0,
+                "edge iterator of empty graph should have no elements"
+            );
+        }
+
+        #[test]
+        fn edges() {
+            let (graph, _, edges, _) = make_test_graph();
+            assert_eq!(graph.edges().count(), 18, "unexpected edge count");
+
+            // Expects each edge to appear exactly once.
+            for e in graph.edges() {
+                assert_eq!(
+                    edges.iter().filter(|&x| *x == e).count(),
+                    1,
+                    "unexpected edge {e:?} from the iterator"
+                );
+            }
+        }
+
+        #[test]
+        fn incidences_empty() {
+            let mut graph = <$T>::new();
+            let v = graph.add_vertex();
+            assert_eq!(
+                graph.incidences(v).count(),
+                0,
+                "incidence iterator of vertex with degree 0 should have no elements"
+            );
+        }
+
+        #[test]
+        fn incidences() {
+            let (graph, vertices, _, incidences) = make_test_graph();
+            for i in 0..10 {
+                assert_eq!(
+                    graph.incidences(vertices[i]).count(),
+                    incidences[i].len(),
+                    "unexpected incidence count for vertex {:?}",
+                    vertices[i]
+                );
+                let mut remaining = incidences[i].clone();
+                for incidence in graph.incidences(vertices[i]) {
+                    let pos = remaining
+                        .iter()
+                        .position(|(v, e)| *v == incidence.0 && *e == incidence.1)
+                        .expect(&format!(
+                            "unexpected incidence {incidence:?} of vertex {:?} from the iterator",
+                            vertices[i]
+                        ));
+                    remaining.swap_remove(pos);
+                }
+                assert!(
+                    remaining.is_empty(),
+                    "expected incidences {:?} of vertex {:?} were not matched by the iterator",
+                    remaining,
+                    vertices[i]
+                );
+            }
+        }
+
+        #[test]
+        fn incidences_edge_consistency() {
+            // For each incidence (v, e) of u, the same edge e must appear in the incidences of v.
+            // For loop edges (u == v), the edge must appear exactly twice in the incidences of u.
+            let (graph, _, _, _) = make_test_graph();
+            for u in graph.vertices() {
+                for (v, e) in graph.incidences(u) {
+                    if u == v {
+                        assert_eq!(
+                            graph.incidences(u).filter(|(_, f)| *f == e).count(),
+                            2,
+                            "loop edge {e:?} should appear exactly twice in incidences of vertex {u:?}"
+                        );
+                    } else {
+                        assert!(
+                            graph.incidences(v).any(|(w, f)| w == u && f == e),
+                            "edge {e:?} from incidences of vertex {u:?} missing in incidences of adjacent vertex {v:?}"
+                        );
+                    }
+                }
+            }
+        }
+
+        #[test]
+        fn incidences_loop_edge() {
+            let mut graph = <$T>::new();
+            let v = graph.add_vertex();
+            let e = graph.add_edge(v, v);
+            let mut iter = graph.incidences(v);
+            assert_eq!(
+                iter.next(),
+                Some((v, e)),
+                "vertex should be adjacent to itself"
+            );
+            assert_eq!(
+                iter.next(),
+                Some((v, e)),
+                "vertex should be adjacent to itself twice"
+            );
+            assert_eq!(
+                iter.next(),
+                None,
+                "too many adjacent vertices from iterator"
+            );
+        }
+
+        #[test]
+        fn incidences_multiple_edges() {
+            let k = 3;
+            let mut graph = <$T>::new();
+            let vertices = [graph.add_vertex(), graph.add_vertex()];
+            let mut edges = Vec::new();
+            for _ in 0..k {
+                edges.push(graph.add_edge(vertices[0], vertices[1]));
+            }
+            for i in 0..2 {
+                let mut iter = graph.incidences(vertices[i]);
+                for j in 0..k {
+                    let current = iter.next().expect(&format!(
+                        "incidence {j} missing, expected {k} incidences for vertex {:?}",
+                        vertices[i]
+                    ));
+                    assert_eq!(
+                        current.0,
+                        vertices[1 - i],
+                        "unexpected adjacent vertex of vertex {:?} in incidence {j}",
+                        vertices[i]
+                    );
+                    assert_eq!(
+                        edges.iter().filter(|e| **e == current.1).count(),
+                        1,
+                        "unexpected incident edge {:?} of vertex {:?}",
+                        current.1,
                         vertices[i],
-                        vertices[1 - i]
                     );
                 }
                 assert_eq!(
@@ -400,7 +585,7 @@ macro_rules! graph_topology_deletion_tests {
 
         #[test]
         fn delete_vertex_connected() {
-            let (mut graph, vertices, _) = make_test_graph();
+            let (mut graph, vertices, _, _) = make_test_graph();
             assert_eq!(
                 graph.vertex_count(),
                 10,
@@ -587,7 +772,7 @@ macro_rules! graph_topology_deletion_tests {
 
         #[test]
         fn vertices_after_delete() {
-            let (mut graph, vertices, _) = make_test_graph();
+            let (mut graph, vertices, _, _) = make_test_graph();
             graph.delete_vertex(vertices[2]);
             assert_eq!(
                 graph.vertex_count(),
@@ -617,7 +802,7 @@ macro_rules! graph_topology_deletion_tests {
 
         #[test]
         fn edges_after_delete() {
-            let (mut graph, vertices, edges) = make_test_graph();
+            let (mut graph, vertices, edges, _) = make_test_graph();
             graph.delete_vertex(vertices[2]);
             assert_eq!(graph.edge_count(), 12, "unexpected edge count after delete");
             assert_eq!(
@@ -640,5 +825,76 @@ macro_rules! graph_topology_deletion_tests {
                 );
             }
         }
+
+        #[test]
+        fn incidences_after_delete_vertex() {
+            let (mut graph, vertices, _, incidences) = make_test_graph();
+            graph.delete_vertex(vertices[2]);
+            for i in [0, 1, 3, 4, 5, 6, 7, 8, 9] {
+                let mut remaining: Vec<_> = incidences[i]
+                    .iter()
+                    .filter(|(v, _)| *v != vertices[2])
+                    .cloned()
+                    .collect();
+                assert_eq!(
+                    graph.incidences(vertices[i]).count(),
+                    remaining.len(),
+                    "unexpected incidence count for vertex {:?} after delete",
+                    vertices[i]
+                );
+                for incidence in graph.incidences(vertices[i]) {
+                    let pos = remaining
+                        .iter()
+                        .position(|(v, e)| *v == incidence.0 && *e == incidence.1)
+                        .expect(&format!(
+                            "unexpected incidence {incidence:?} of vertex {:?} after delete",
+                            vertices[i]
+                        ));
+                    remaining.swap_remove(pos);
+                }
+                assert!(
+                    remaining.is_empty(),
+                    "expected incidences {:?} of vertex {:?} not matched after delete",
+                    remaining,
+                    vertices[i]
+                );
+            }
+        }
+
+        #[test]
+        fn incidences_after_delete_edge() {
+            let (mut graph, vertices, edges, incidences) = make_test_graph();
+            // Deletes the edge from vertices[1] to vertices[2].
+            graph.delete_edge(edges[2]);
+            for i in 0..10 {
+                let mut remaining: Vec<_> = incidences[i]
+                    .iter()
+                    .filter(|(_, e)| *e != edges[2])
+                    .cloned()
+                    .collect();
+                assert_eq!(
+                    graph.incidences(vertices[i]).count(),
+                    remaining.len(),
+                    "unexpected incidence count for vertex {:?} after delete",
+                    vertices[i]
+                );
+                for incidence in graph.incidences(vertices[i]) {
+                    let pos = remaining
+                        .iter()
+                        .position(|(v, e)| *v == incidence.0 && *e == incidence.1)
+                        .expect(&format!(
+                            "unexpected incidence {incidence:?} of vertex {:?} after delete",
+                            vertices[i]
+                        ));
+                    remaining.swap_remove(pos);
+                }
+                assert!(
+                    remaining.is_empty(),
+                    "expected incidences {:?} of vertex {:?} not matched after delete",
+                    remaining,
+                    vertices[i]
+                );
+            }
+        }
     };
 }

src/traits.rs

@@ -19,6 +19,7 @@ pub trait GraphTopology {
     fn vertices(&self) -> impl Iterator<Item = Self::Vertex>;
     fn adjacent_vertices(&self, v: Self::Vertex) -> impl Iterator<Item = 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;
     fn add_edge(&mut self, v1: Self::Vertex, v2: Self::Vertex) -> Self::Edge;
 }