diff --git a/onnxruntime/core/providers/dml/DmlExecutionProvider/src/DmlGraphDeserialization.cpp b/onnxruntime/core/providers/dml/DmlExecutionProvider/src/DmlGraphDeserialization.cpp
index 7d8ed17e7d925..128123fa32f12 100644
--- a/onnxruntime/core/providers/dml/DmlExecutionProvider/src/DmlGraphDeserialization.cpp
+++ b/onnxruntime/core/providers/dml/DmlExecutionProvider/src/DmlGraphDeserialization.cpp
@@ -415,7 +415,7 @@ template <typename EdgeType> void PopulateEdges(
                 if (edgeToOutgoingNodeIndexMap.find(edgeName->string_view()) == edgeToOutgoingNodeIndexMap.end())
                 {
                     throw std::range_error("Neither there is any graph input with name " + edgeName->str() + 
-                                           "nor there is any node which has " + edgeName->str() + " as one of the output.");
+                                           " nor there is any node which has " + edgeName->str() + " as one of the output.");
                 }
                 auto& intermediateEdgeNodeIndex = edgeToOutgoingNodeIndexMap[edgeName->string_view()];
                 DmlIntermediateSerializedGraphEdge intermediateEdge = {};
@@ -464,17 +464,11 @@ DmlSerializedGraphDesc DeserializeDmlGraph(
     std::vector<DmlOutputSerializedGraphEdge> outputEdges;
     std::vector<DmlIntermediateSerializedGraphEdge> intermediateEdges;
 
+    // Iterate the output edges first because nodes are not in topologically sorted.
     for (uint32_t nodeIndex = 0; nodeIndex < flatbufferGraphDesc->nodes()->size(); nodeIndex++)
     {
         const dml::ir::DmlGraphNode* flatbufferNode = flatbufferGraphDesc->nodes()->Get(nodeIndex);
 
-        PopulateEdges<DmlInputSerializedGraphEdge>(
-            nodeIndex,
-            flatbufferNode->inputNames(),
-            graphInputEdgeToIndexMap,
-            inputEdges,
-            intermediateEdges,
-            edgeToOutgoingNodeIndexMap);
         PopulateEdges<DmlOutputSerializedGraphEdge>(
             nodeIndex,
             flatbufferNode->outputNames(),
@@ -482,7 +476,20 @@ DmlSerializedGraphDesc DeserializeDmlGraph(
             outputEdges,
             intermediateEdges,
             edgeToOutgoingNodeIndexMap);
+    }
+
+    for (uint32_t nodeIndex = 0; nodeIndex < flatbufferGraphDesc->nodes()->size(); nodeIndex++)
+    {
+        const dml::ir::DmlGraphNode* flatbufferNode = flatbufferGraphDesc->nodes()->Get(nodeIndex);
 
+        PopulateEdges<DmlInputSerializedGraphEdge>(
+            nodeIndex,
+            flatbufferNode->inputNames(),
+            graphInputEdgeToIndexMap,
+            inputEdges,
+            intermediateEdges,
+            edgeToOutgoingNodeIndexMap);
+        
         DmlSerializedGraphNode node = {};
         if (flatbufferNode->name()->size() == 0)
         {
diff --git a/onnxruntime/core/providers/dml/DmlExecutionProvider/src/GraphDescBuilder.cpp b/onnxruntime/core/providers/dml/DmlExecutionProvider/src/GraphDescBuilder.cpp
index e6f008af5c23f..f8347544a32be 100644
--- a/onnxruntime/core/providers/dml/DmlExecutionProvider/src/GraphDescBuilder.cpp
+++ b/onnxruntime/core/providers/dml/DmlExecutionProvider/src/GraphDescBuilder.cpp
@@ -140,6 +140,16 @@ namespace Dml::GraphDescBuilder
         {
             intermediateEdge.FromNodeIndex = shiftedIndicesMapping[intermediateEdge.FromNodeIndex];
             intermediateEdge.ToNodeIndex = shiftedIndicesMapping[intermediateEdge.ToNodeIndex];
+            std::string oldEdgeName = intermediateEdge.Name;
+            size_t pos = oldEdgeName.find("nodeIdx:");
+            if (pos != std::string::npos)
+            {
+                if (pos != 0)
+                {
+                    intermediateEdge.Name = oldEdgeName.substr(0, pos);
+                }
+                intermediateEdge.Name += "nodeIdx:" + std::to_string(intermediateEdge.FromNodeIndex) + "-outputIdx:" + std::to_string(intermediateEdge.FromNodeOutputIndex);
+            }
         }
     }