diff --git a/src/generators.rs b/src/generators.rs
index 5dc36e7..5eb62b7 100644
--- a/src/generators.rs
+++ b/src/generators.rs
@@ -84,37 +84,128 @@ where
 
 #[cfg(test)]
 mod tests {
+    use std::fmt::Debug;
+
     use super::*;
+    use crate::models::{FrozenGraph, Graph};
 
     #[test]
-    fn petersen() {
-        let mut graph = AppendGraph::new();
-        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");
+    fn petersen_append_graph() {
+        petersen_add::<AppendGraph>();
+    }
+
+    #[test]
+    fn petersen_graph() {
+        petersen_add::<Graph>();
+    }
+
+    #[test]
+    fn petersen_frozen_graph() {
+        petersen_generate_as::<FrozenGraph>();
+    }
+
+    fn petersen_generate_as<G: GraphTopologyConversion>()
+    where
+        G::Vertex: Debug,
+        G::Edge: Debug,
+    {
+        let (graph, vertices, edges) = generate_as::<G, _, _>(petersen);
+        assert_petersen(&graph, &vertices, &edges);
+    }
+
+    fn petersen_add<G: GraphTopologyAddition>()
+    where
+        G::Vertex: Debug,
+        G::Edge: Debug,
+    {
+        let mut graph = G::default();
+        let (vertices, edges) = petersen(&mut graph);
+        assert_petersen(&graph, &vertices, &edges);
+    }
+
+    fn assert_petersen<G: GraphTopology>(graph: &G, vertices: &[G::Vertex], edges: &[G::Edge])
+    where
+        G::Vertex: Debug,
+        G::Edge: Debug,
+    {
+        assert_element_counts(graph, 10, 15);
+        assert_handles(graph.vertices(), vertices, "vertex");
+        assert_handles(graph.edges(), edges, "edge");
+        assert_no_loops_no_multi_edges(graph);
         assert!(
             graph.vertices().all(|v| graph.degree(v) == 3),
             "all vertices should have degree 3"
         );
-        assert_handles_in_graph(&graph, &vertices, &edges);
+        // 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 vertices.iter().enumerate() {
+            for &u in &vertices[i + 1..] {
+                if graph.are_adjacent(v, u) {
+                    assert!(
+                        graph.common_neighbors(u, v).next().is_none(),
+                        "adjacent vertices {u:?} and {v:?} should not have a common neighbor"
+                    );
+                } else {
+                    assert_eq!(
+                        graph.common_neighbors(u, v).count(),
+                        1,
+                        "non-adjacent vertices {u:?} and {v:?} should have exactly one common neighbor"
+                    );
+                }
+            }
+        }
     }
 
-    fn assert_handles_in_graph<G: GraphTopology>(
+    fn assert_element_counts<G: GraphTopology>(
         graph: &G,
-        vertices: &[G::Vertex],
-        edges: &[G::Edge],
+        expected_vertex_count: usize,
+        expected_edge_count: usize,
     ) {
-        assert!(
-            vertices.iter().all(|&v| graph.vertices().any(|u| u == v)),
-            "all returned vertices should be in the graph"
+        assert_eq!(
+            graph.vertex_count(),
+            expected_vertex_count,
+            "unexpected number of vertices"
         );
-        assert!(
-            edges.iter().all(|&e| graph.edges().any(|f| f == e)),
-            "all returned edges should be in the graph"
+        assert_eq!(
+            graph.edge_count(),
+            expected_edge_count,
+            "unexpected number of 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_no_multi_edges<G: GraphTopology>(graph: &G)
+    where
+        G::Vertex: Debug,
+        G::Edge: Debug,
+    {
+        for e in graph.edges() {
+            let (u, v) = graph.incident_vertices(e);
+            assert_ne!(u, v, "unexpected loop edge {e:?}");
+        }
+        for v in graph.vertices() {
+            let mut neighbors = Vec::new();
+            for u in graph.adjacent_vertices(v) {
+                assert!(
+                    !neighbors.contains(&u),
+                    "unexpected multi-edge between {v:?} and {u:?}"
+                );
+                neighbors.push(u);
+            }
+        }
+    }
 }