diff --git a/src/backend/base/langflow/graph/graph/base.py b/src/backend/base/langflow/graph/graph/base.py
index a83a971b5..cd761bbff 100644
--- a/src/backend/base/langflow/graph/graph/base.py
+++ b/src/backend/base/langflow/graph/graph/base.py
@@ -1236,9 +1236,11 @@ class Graph:
                                 stack.append(successor.id)
                             else:
                                 excluded.add(successor.id)
-                elif current_id not in stop_predecessors:
+                elif current_id not in stop_predecessors and is_start:
                     # If the current vertex is not the target vertex, we should add all its successors
                     # to the stack if they are not in visited
+
+                    # If we are starting from the beginning, we should add all successors
                     for successor in current_vertex.successors:
                         if successor.id not in visited:
                             stack.append(successor.id)