diff --git a/src/backend/base/langflow/api/v1/chat.py b/src/backend/base/langflow/api/v1/chat.py
index bbc183da8..7e933d1df 100644
--- a/src/backend/base/langflow/api/v1/chat.py
+++ b/src/backend/base/langflow/api/v1/chat.py
@@ -110,7 +110,7 @@ async def retrieve_vertices_order(
         # We need to get the id of each vertex
         # and return the same structure but only with the ids
         components_count = len(graph.vertices)
-        vertices_to_run = list(graph.vertices_to_run) + get_top_level_vertices(graph, graph.vertices_to_run)
+        vertices_to_run = list(graph.vertices_to_run.union(get_top_level_vertices(graph, graph.vertices_to_run)))
         await chat_service.set_cache(str(flow_id), graph)
         background_tasks.add_task(
             telemetry_service.log_package_playground,
diff --git a/src/backend/base/langflow/graph/graph/base.py b/src/backend/base/langflow/graph/graph/base.py
index 1b383f7e9..b67b2733c 100644
--- a/src/backend/base/langflow/graph/graph/base.py
+++ b/src/backend/base/langflow/graph/graph/base.py
@@ -134,9 +134,10 @@ class Graph:
         vertices_ids = set()
         new_predecessor_map = {}
         for vertex_id in self._is_state_vertices:
-            if vertex_id == caller:
-                continue
+            caller_vertex = self.get_vertex(caller)
             vertex = self.get_vertex(vertex_id)
+            if vertex_id == caller or vertex.display_name == caller_vertex.display_name:
+                continue
             if (
                 isinstance(vertex._raw_params["name"], str)
                 and name in vertex._raw_params["name"]
@@ -152,15 +153,17 @@ class Graph:
                 # and run self.build_adjacency_maps(edges) to get the new predecessor map
                 # that is not complete but we can use to update the run_predecessors
                 edges_set = set()
-                for vertex in [vertex] + successors:
-                    edges_set.update(vertex.edges)
-                    vertices_ids.add(vertex.id)
-                    if vertex.state == VertexStates.INACTIVE:
-                        vertex.set_state("ACTIVE")
+                for _vertex in [vertex] + successors:
+                    edges_set.update(_vertex.edges)
+                    if _vertex.state == VertexStates.INACTIVE:
+                        _vertex.set_state("ACTIVE")
                 edges = list(edges_set)
                 predecessor_map, _ = self.build_adjacency_maps(edges)
                 new_predecessor_map.update(predecessor_map)
 
+        # vertices_ids.update(new_predecessor_map.keys())
+        # vertices_ids.update(v_id for value_list in new_predecessor_map.values() for v_id in value_list)
+
         self.activated_vertices = list(vertices_ids)
         self.vertices_to_run.update(vertices_ids)
         self.run_manager.update_run_state(
@@ -861,6 +864,7 @@ class Graph:
             ValueError: If no result is found for the vertex.
         """
         vertex = self.get_vertex(vertex_id)
+        self.run_manager.add_to_vertices_being_run(vertex_id)
         try:
             params = ""
             if vertex.frozen:
@@ -1494,8 +1498,6 @@ class Graph:
         predecessor_map: dict[str, list[str]] = defaultdict(list)
         successor_map: dict[str, list[str]] = defaultdict(list)
         for edge in edges:
-            if edge.source_id not in predecessor_map[edge.target_id]:
-                predecessor_map[edge.target_id].append(edge.source_id)
-            if edge.target_id not in successor_map[edge.source_id]:
-                successor_map[edge.source_id].append(edge.target_id)
+            predecessor_map[edge.target_id].append(edge.source_id)
+            successor_map[edge.source_id].append(edge.target_id)
         return predecessor_map, successor_map
diff --git a/src/backend/base/langflow/graph/graph/runnable_vertices_manager.py b/src/backend/base/langflow/graph/graph/runnable_vertices_manager.py
index fc9970554..01c80e06a 100644
--- a/src/backend/base/langflow/graph/graph/runnable_vertices_manager.py
+++ b/src/backend/base/langflow/graph/graph/runnable_vertices_manager.py
@@ -12,6 +12,7 @@ class RunnableVerticesManager:
         self.run_map = defaultdict(list)  # Tracks successors of each vertex
         self.run_predecessors = defaultdict(set)  # Tracks predecessors for each vertex
         self.vertices_to_run = set()  # Set of vertices that are ready to run
+        self.vertices_being_run = set()  # Set of vertices that are currently running
 
     def to_dict(self) -> dict:
         return {
@@ -49,7 +50,7 @@ class RunnableVerticesManager:
         """Determines if a vertex is runnable."""
 
         return (
-            vertex_id in self.vertices_to_run
+            vertex_id not in self.vertices_being_run
             and not self.run_predecessors.get(vertex_id)
             and vertex_id not in inactivated_vertices
         )
@@ -88,6 +89,7 @@ class RunnableVerticesManager:
             self.vertices_to_run.add(vertex_id)
         else:
             self.vertices_to_run.discard(vertex_id)
+            self.vertices_being_run.discard(vertex_id)
 
     async def get_next_runnable_vertices(
         self,
@@ -125,7 +127,10 @@ class RunnableVerticesManager:
                 next_runnable_vertices = direct_successors_ready
 
             for v_id in set(next_runnable_vertices):  # Use set to avoid duplicates
-                self.remove_vertex_from_runnables(v_id)
+                if vertex.id == v_id:
+                    next_runnable_vertices.remove(v_id)
+                else:
+                    self.add_to_vertices_being_run(v_id)
             if cache:
                 await set_cache_coro(data=graph, lock=lock)  # type: ignore
         return next_runnable_vertices
@@ -134,6 +139,9 @@ class RunnableVerticesManager:
         self.update_vertex_run_state(v_id, is_runnable=False)
         self.remove_from_predecessors(v_id)
 
+    def add_to_vertices_being_run(self, v_id):
+        self.vertices_being_run.add(v_id)
+
     @staticmethod
     def get_top_level_vertices(graph, vertices_ids):
         """