diff --git a/src/testing/fixtures.rs b/src/testing/fixtures.rs
index f60dcf3..048d088 100644
--- a/src/testing/fixtures.rs
+++ b/src/testing/fixtures.rs
@@ -338,3 +338,143 @@ where
     }
     path
 }
+
+/// Asserts that the two graphs are isomorphic.
+///
+/// `vertices` must contain all vertices of the `original` graph, and `vertex_map` must for any
+/// vertex in the `original` graph return the corresponding vertex in the `other` graph.
+///
+/// `edges` must contain all edges and their endpoints of the `original` graph, and `edge_map` must
+/// for any edge in the `original` graph return the corresponding edge in the `other` graph.
+pub fn assert_isomorphic<G: GraphTopology, H: GraphTopology>(
+    original: &G,
+    other: &H,
+    vertices: &[G::Vertex],
+    vertex_map: impl Fn(G::Vertex) -> H::Vertex,
+    edges: &[(G::Edge, G::Vertex, G::Vertex)],
+    edge_map: impl Fn(G::Edge) -> H::Edge,
+) where
+    G::Vertex: Debug,
+    G::Edge: Debug,
+    H::Vertex: Debug,
+    H::Edge: Debug,
+{
+    assert_eq!(
+        original.vertex_count(),
+        vertices.len(),
+        "precondition: all vertices of the original must be provided"
+    );
+    assert_eq!(
+        original.edge_count(),
+        edges.len(),
+        "precondition: all edges of the original must be provided"
+    );
+    assert_eq!(
+        other.vertex_count(),
+        original.vertex_count(),
+        "other graph should have the same vertex count as the original"
+    );
+    assert_eq!(
+        other.edge_count(),
+        original.edge_count(),
+        "other graph should have the same edge count as the original"
+    );
+    for &v in vertices.iter() {
+        assert_eq!(
+            other.degree(vertex_map(v)),
+            original.degree(v),
+            "vertex {v:?} should have the same degree in the other graph as in the original"
+        );
+        let mut expected: Vec<_> = original.incidences(v).collect();
+        for incidence in other.incidences(vertex_map(v)) {
+            let pos = expected
+                .iter()
+                .position(|x| {
+                    vertex_map(x.vertex) == incidence.vertex && edge_map(x.edge) == incidence.edge
+                })
+                .expect(&format!(
+                    "unexpected incidence {incidence:?} of vertex {v:?} in the other graph"
+                ));
+            expected.swap_remove(pos);
+        }
+        assert!(
+            expected.is_empty(),
+            "expected incidences {expected:?} of vertex {v:?} are missing in the other graph"
+        );
+    }
+    for &(e, u, v) in edges.iter() {
+        assert_eq!(
+            other.incident_vertices(edge_map(e)),
+            (vertex_map(u), vertex_map(v)),
+            "edge {e:?} should have the same incident vertices in the other graph as in the original"
+        );
+    }
+}
+
+/// Asserts that mutation of the two graphs happens independently.
+///
+/// `vertices` must contain all vertices of the `original` graph, which must not be empty, and
+/// `vertex_map` must for any vertex in the `original` graph return the corresponding vertex in the
+/// `other` graph.
+pub fn assert_mutation_independent<G: GraphTopologyAddition, H: GraphTopologyAddition>(
+    original: &mut G,
+    other: &mut H,
+    vertices: &[G::Vertex],
+    vertex_map: impl Fn(G::Vertex) -> H::Vertex,
+) {
+    let edge_count = original.edge_count();
+    assert_eq!(
+        original.vertex_count(),
+        vertices.len(),
+        "precondition: all vertices of the original must be provided"
+    );
+    assert!(
+        !vertices.is_empty(),
+        "precondition: at least one vertex must be provided"
+    );
+    let u = other.add_vertex();
+    other.add_edge(vertex_map(vertices[0]), u);
+    assert_eq!(
+        other.vertex_count(),
+        vertices.len() + 1,
+        "precondition: vertex count of other graph"
+    );
+    assert_eq!(
+        other.edge_count(),
+        edge_count + 1,
+        "precondition: edge count of other graph"
+    );
+    assert_eq!(
+        original.vertex_count(),
+        vertices.len(),
+        "mutating the other graph should not affect the vertex count of the original"
+    );
+    assert_eq!(
+        original.edge_count(),
+        edge_count,
+        "mutating the other graph should not affect the edge count of the original"
+    );
+
+    let v = original.add_vertex();
+    original.add_edge(vertices[0], v);
+    assert_eq!(
+        original.vertex_count(),
+        vertices.len() + 1,
+        "precondition: vertex count of original"
+    );
+    assert_eq!(
+        original.edge_count(),
+        edge_count + 1,
+        "precondition: edge count of original"
+    );
+    assert_eq!(
+        other.vertex_count(),
+        vertices.len() + 1,
+        "mutating the original should not affect the vertex count of the other graph"
+    );
+    assert_eq!(
+        other.edge_count(),
+        edge_count + 1,
+        "mutating the original should not affect the edge count of the other graph"
+    );
+}
diff --git a/src/testing/graph_topology_addition_clone_testing.rs b/src/testing/graph_topology_addition_clone_testing.rs
index b476dfe..2f360eb 100644
--- a/src/testing/graph_topology_addition_clone_testing.rs
+++ b/src/testing/graph_topology_addition_clone_testing.rs
@@ -1,3 +1,4 @@
+use crate::testing::fixtures;
 use crate::testing::fixtures::MakeTestGraph;
 use crate::traits::GraphTopologyAddition;
 
@@ -6,7 +7,7 @@ use crate::traits::GraphTopologyAddition;
 macro_rules! graph_topology_addition_clone_tests {
     ($T:ty) => {
         $crate::graph_topology_addition_clone_tests!(@wrap $T,
-            clone_independent,
+            clone_mutation_independent,
         );
     };
 
@@ -20,37 +21,8 @@ macro_rules! graph_topology_addition_clone_tests {
     };
 }
 
-pub fn clone_independent<G: Clone + GraphTopologyAddition>() {
-    let (mut graph, [u, v], _) = G::single_edge();
+pub fn clone_mutation_independent<G: Clone + GraphTopologyAddition>() {
+    let (mut graph, vertices, _) = G::single_edge();
     let mut clone = graph.clone();
-
-    let w = clone.add_vertex();
-    clone.add_edge(u, w);
-    assert_eq!(clone.vertex_count(), 3, "precondition: vertex count of clone");
-    assert_eq!(clone.edge_count(), 2, "precondition: edge count of clone");
-    assert_eq!(
-        graph.vertex_count(),
-        2,
-        "mutating the clone should not affect the vertex count of the original"
-    );
-    assert_eq!(
-        graph.edge_count(),
-        1,
-        "mutating the clone should not affect the edge count of the original"
-    );
-
-    let x = graph.add_vertex();
-    graph.add_edge(v, x);
-    assert_eq!(graph.vertex_count(), 3, "precondition: vertex count of original");
-    assert_eq!(graph.edge_count(), 2, "precondition: edge count of original");
-    assert_eq!(
-        clone.vertex_count(),
-        3,
-        "mutating the original should not affect the vertex count of the clone"
-    );
-    assert_eq!(
-        clone.edge_count(),
-        2,
-        "mutating the original should not affect the edge count of the clone"
-    );
+    fixtures::assert_mutation_independent(&mut graph, &mut clone, &vertices, |v| v);
 }
diff --git a/src/testing/graph_topology_clone_testing.rs b/src/testing/graph_topology_clone_testing.rs
index 12b9606..b4ffd1e 100644
--- a/src/testing/graph_topology_clone_testing.rs
+++ b/src/testing/graph_topology_clone_testing.rs
@@ -1,5 +1,6 @@
 use std::fmt::Debug;
 
+use crate::testing::fixtures;
 use crate::testing::fixtures::MakeTestGraph;
 
 #[doc(hidden)]
@@ -7,7 +8,6 @@ use crate::testing::fixtures::MakeTestGraph;
 macro_rules! graph_topology_clone_tests {
     ($T:ty) => {
         $crate::graph_topology_clone_tests!(@wrap $T,
-            clone_preserves_vertex_and_edge_count,
             clone_handles_interchangeable,
         );
     };
@@ -22,21 +22,6 @@ macro_rules! graph_topology_clone_tests {
     };
 }
 
-pub fn clone_preserves_vertex_and_edge_count<G: Clone + MakeTestGraph>() {
-    let (graph, ..) = G::standard();
-    let clone = graph.clone();
-    assert_eq!(
-        clone.vertex_count(),
-        graph.vertex_count(),
-        "clone should have the same vertex count as the original"
-    );
-    assert_eq!(
-        clone.edge_count(),
-        graph.edge_count(),
-        "clone should have the same edge count as the original"
-    );
-}
-
 /// Queries the clone using vertex and edge handles obtained from the original graph, and asserts
 /// that the results are identical to querying the original with those same handles. This is only
 /// meaningful because Vertex and Edge handles are not tied to a particular graph instance.
@@ -47,32 +32,5 @@ where
 {
     let (graph, vertices, edges, _) = G::standard();
     let clone = graph.clone();
-    for &v in vertices.iter() {
-        assert_eq!(
-            clone.degree(v),
-            graph.degree(v),
-            "vertex {v:?} should have the same degree in the clone as in the original"
-        );
-        let mut expected: Vec<_> = graph.incidences(v).collect();
-        for incidence in clone.incidences(v) {
-            let pos = expected
-                .iter()
-                .position(|x| *x == incidence)
-                .expect(&format!(
-                    "unexpected incidence {incidence:?} of vertex {v:?} in the clone"
-                ));
-            expected.swap_remove(pos);
-        }
-        assert!(
-            expected.is_empty(),
-            "expected incidences {expected:?} of vertex {v:?} are missing in the clone"
-        );
-    }
-    for &(e, u, v) in edges.iter() {
-        assert_eq!(
-            clone.incident_vertices(e),
-            (u, v),
-            "edge {e:?} should have the same incident vertices in the clone as in the original"
-        );
-    }
+    fixtures::assert_isomorphic(&graph, &clone, &vertices, |v| v, &edges, |e| e);
 }