diff --git a/onnxruntime/core/providers/dml/DmlExecutionProvider/src/GraphDescBuilder.cpp b/onnxruntime/core/providers/dml/DmlExecutionProvider/src/GraphDescBuilder.cpp
index 898df7a11b..6b9230657b 100644
--- a/onnxruntime/core/providers/dml/DmlExecutionProvider/src/GraphDescBuilder.cpp
+++ b/onnxruntime/core/providers/dml/DmlExecutionProvider/src/GraphDescBuilder.cpp
@@ -95,6 +95,13 @@ namespace Dml::GraphDescBuilder
             }
         }
 
+        // Delete the edges that reference nodes that are not reachable before removing the nodes themselves
+        graphIntermediateEdges.erase(
+            std::remove_if(graphIntermediateEdges.begin(), graphIntermediateEdges.end(), [&nodesData](const auto& intermediateEdge){
+                return nodesData[intermediateEdge.FromNodeIndex].state == NodeState::NotVisited || nodesData[intermediateEdge.ToNodeIndex].state == NodeState::NotVisited;
+            }),
+            graphIntermediateEdges.end());
+
         // Mapping from the old indices to the new indices that have been shifted after removing earlier nodes
         std::vector<uint32_t> shiftedIndicesMapping(graphNodes.size());
 
@@ -134,12 +141,6 @@ namespace Dml::GraphDescBuilder
             intermediateEdge.FromNodeIndex = shiftedIndicesMapping[intermediateEdge.FromNodeIndex];
             intermediateEdge.ToNodeIndex = shiftedIndicesMapping[intermediateEdge.ToNodeIndex];
         }
-
-        graphIntermediateEdges.erase(
-            std::remove_if(graphIntermediateEdges.begin(), graphIntermediateEdges.end(), [&nodesData](const auto& intermediateEdge){
-                return nodesData[intermediateEdge.FromNodeIndex].state == NodeState::NotVisited || nodesData[intermediateEdge.ToNodeIndex].state == NodeState::NotVisited;
-            }),
-            graphIntermediateEdges.end());
     }
 
     GraphDesc BuildGraphDesc(