diff --git a/src/semra/api.py b/src/semra/api.py
index 15f17fe0..97fbe26a 100644
--- a/src/semra/api.py
+++ b/src/semra/api.py
@@ -17,7 +17,7 @@
 from ssslm import LiteralMapping
 from tqdm.auto import tqdm
 
-from semra.io.graph import _from_digraph_edge, to_digraph
+from semra.io.graph import to_digraph, to_simple_graph
 from semra.rules import EXACT_MATCH, FLIP, INVERSION_MAPPING, SubsetConfiguration
 from semra.struct import (
     Evidence,
@@ -559,19 +559,31 @@ def prioritize(
     >>> prioritize(mappings, ["mesh", "doid", "umls"])
     """
     original_mappings = len(mappings)
-    mappings = [m for m in mappings if m.predicate == EXACT_MATCH]
+    mappings_by_subj_obj: dict[tuple[str, str], Mapping] = {
+        (mapping.subject.curie, mapping.object.curie): mapping
+        for mapping in mappings
+        if mapping.predicate == EXACT_MATCH
+    }
+    # Gather all the references by CURIE
+    curie_to_reference: dict[str, Reference] = {
+        reference.curie: reference
+        for mapping in mappings
+        for reference in (mapping.subject, mapping.object)
+    }
+
     exact_mappings = len(mappings)
     priority = _clean_priority_prefixes(priority)
 
-    graph = to_digraph(mappings).to_undirected()
+    graph = to_simple_graph(mappings)
     rv: list[Mapping] = []
     for component in tqdm(
         nx.connected_components(graph), unit="component", unit_scale=True, disable=not progress
     ):
-        o = get_priority_reference(component, priority)
+        component_references = [curie_to_reference[curie] for curie in component]
+        o = get_priority_reference(component_references, priority)
         if o is None:
             continue
-        for s in component:
+        for s in component_references:
             if s == o:  # don't add self-edges
                 continue
             if not graph.has_edge(s, o):
@@ -583,7 +595,7 @@ def prioritize(
                     "that in a given component, it is a full clique (i.e., there are edges "
                     "in both directions between all nodes)"
                 )
-            rv.extend(_from_digraph_edge(graph, s, o))
+            rv.append(mappings_by_subj_obj[s.curie, o.curie])
 
     # sort such that the mappings are ordered by object by priority order
     # then identifier of object, then subject prefix in alphabetical order
diff --git a/src/semra/io/graph.py b/src/semra/io/graph.py
index 0362448a..53d8c13f 100644
--- a/src/semra/io/graph.py
+++ b/src/semra/io/graph.py
@@ -17,6 +17,7 @@
     "from_multidigraph",
     "to_digraph",
     "to_multidigraph",
+    "to_simple_graph",
 ]
 
 #: The key inside the data dictionary for a SeMRA mapping graph
@@ -56,6 +57,21 @@ def to_digraph(mappings: t.Iterable[Mapping]) -> nx.DiGraph:
     return graph
 
 
+def to_simple_graph(mappings: t.Iterable[Mapping]) -> nx.Graph:
+    """Return an undirected graph capturing only the structure of mappings.
+
+    :param mappings: An iterable of mappings
+
+    :returns: An undirected graph in which the nodes are simple string CURIEs
+        corresponding to References. The edges are undirected and represent
+        the relationships between subject and object CURIEs in mappings.
+    """
+    graph = nx.Graph()
+    edges = {(mapping.subject.curie, mapping.object.curie) for mapping in mappings}
+    graph.add_edges_from(edges)
+    return graph
+
+
 def from_digraph(graph: nx.DiGraph) -> list[Mapping]:
     """Extract mappings from a simple directed graph data model."""
     return [mapping for s, o in graph.edges() for mapping in _from_digraph_edge(graph, s, o)]