diff --git a/graphify/export.py b/graphify/export.py
index 12d114404..ff2133364 100644
--- a/graphify/export.py
+++ b/graphify/export.py
@@ -1346,9 +1346,12 @@ def to_graphml(
     for node_id in H.nodes():
         for key, val in list(H.nodes[node_id].items()):
             H.nodes[node_id][key] = _graphml_safe(val)
-    for u, v in H.edges():
-        for key, val in list(H.edges[u, v].items()):
-            H.edges[u, v][key] = _graphml_safe(val)
+    # edges(data=True) rather than H.edges[u, v]: graph.json is loaded as a
+    # MultiGraph when it carries parallel edges (#4500), and a MultiGraph edge
+    # view needs a key, so the (u, v) form crashed the whole export.
+    for *_, attrs in H.edges(data=True):
+        for key, val in list(attrs.items()):
+            attrs[key] = _graphml_safe(val)
 
     # Write atomically: a mid-serialization error otherwise leaves a 0-byte
     # .graphml on disk that downstream tooling mistakes for a completed export
diff --git a/tests/test_export.py b/tests/test_export.py
index 61c4c066f..7cc95f045 100644
--- a/tests/test_export.py
+++ b/tests/test_export.py
@@ -282,6 +282,30 @@ def test_to_graphml_tolerates_dict_and_list_attribute_values():
         assert not (Path(tmp) / "graph.graphml.tmp").exists()
 
 
+def test_to_graphml_exports_multigraph_parallel_edges():
+    """graph.json is loaded as a MultiGraph when it carries parallel edges
+    (#4500), e.g. `imports` and `calls` between the same two nodes. The edge
+    coercion loop indexed H.edges[u, v], which needs a key on a MultiGraph, so
+    the export crashed; every parallel edge must reach the file, coerced."""
+    import networkx as nx
+    G = nx.MultiGraph()
+    G.add_node("a", label="A")
+    G.add_node("b", label="B")
+    G.add_edge("a", "b", relation="imports", confidence="EXTRACTED", note=None)
+    G.add_edge("a", "b", relation="calls", confidence="INFERRED", ctx={"k": "v"})
+    with tempfile.TemporaryDirectory() as tmp:
+        out = Path(tmp) / "g.graphml"
+        to_graphml(G, {0: ["a", "b"]}, str(out))
+        H = nx.read_graphml(str(out))
+        assert H.number_of_edges() == 2
+        edges = [d for _, _, d in H.edges(data=True)]
+        assert sorted(d["relation"] for d in edges) == ["calls", "imports"]
+        calls = next(d for d in edges if d["relation"] == "calls")
+        imports = next(d for d in edges if d["relation"] == "imports")
+        assert json.loads(calls["ctx"]) == {"k": "v"}
+        assert imports["note"] == ""
+
+
 def test_to_graphml_preserves_native_scalar_types():
     """Coercion must leave GraphML-native scalars (int/float/bool/str) untouched,
     only stringifying non-scalars (#1831)."""