diff --git a/common/workflow-operator/src/main/scala/org/apache/texera/amber/operator/visualization/networkGraph/NetworkGraphOpDesc.scala b/common/workflow-operator/src/main/scala/org/apache/texera/amber/operator/visualization/networkGraph/NetworkGraphOpDesc.scala
index ccbf51c7377..789a6b5bb3c 100644
--- a/common/workflow-operator/src/main/scala/org/apache/texera/amber/operator/visualization/networkGraph/NetworkGraphOpDesc.scala
+++ b/common/workflow-operator/src/main/scala/org/apache/texera/amber/operator/visualization/networkGraph/NetworkGraphOpDesc.scala
@@ -98,7 +98,9 @@ class NetworkGraphOpDesc extends PythonOperatorDescriptor {
          |        if not table.empty:
          |            sources = table[$source]
          |            destinations = table[$destination]
-         |            nodes = set(sources + destinations)
+         |            # Union of the two columns, in first-appearance order. Adding the
+         |            # Series pairs them off element-wise; a set reorders per run.
+         |            nodes = list(dict.fromkeys(pd.concat([sources, destinations]).tolist()))
          |            G = nx.Graph()
          |            for node in nodes:
          |                G.add_node(node)
diff --git a/common/workflow-operator/src/test/scala/org/apache/texera/amber/operator/visualization/networkGraph/NetworkGraphOpDescSpec.scala b/common/workflow-operator/src/test/scala/org/apache/texera/amber/operator/visualization/networkGraph/NetworkGraphOpDescSpec.scala
index 840b62b6431..fc666c61abd 100644
--- a/common/workflow-operator/src/test/scala/org/apache/texera/amber/operator/visualization/networkGraph/NetworkGraphOpDescSpec.scala
+++ b/common/workflow-operator/src/test/scala/org/apache/texera/amber/operator/visualization/networkGraph/NetworkGraphOpDescSpec.scala
@@ -85,4 +85,19 @@ class NetworkGraphOpDescSpec extends AnyFlatSpec with BeforeAndAfter with Matche
     assert(carries(code, "My Graph"))
     code should include("class ProcessTableOperator(UDFTableOperator)")
   }
+
+  it should "build the node set as a union rather than by adding the two columns" in {
+    opDesc.source = "from_node"
+    opDesc.destination = "to_node"
+    val code = opDesc.generatePythonCode()
+
+    // `sources + destinations` is element-wise on two Series, so it glued each
+    // source to its destination and those strings entered the graph as nodes.
+    code should not include "set(sources + destinations)"
+    code should include("pd.concat([sources, destinations])")
+
+    // Ordered de-duplication, not a set: a set iterates strings in an order that
+    // varies between processes, which would move the nodes from run to run.
+    code should include("dict.fromkeys")
+  }
 }