diff --git a/src/backend/langflow/graph/graph/base.py b/src/backend/langflow/graph/graph/base.py
index 68e16bed8..341a4729c 100644
--- a/src/backend/langflow/graph/graph/base.py
+++ b/src/backend/langflow/graph/graph/base.py
@@ -1,3 +1,4 @@
+import asyncio
 from collections import defaultdict, deque
 from typing import TYPE_CHECKING, Dict, Generator, List, Optional, Type, Union
 
@@ -40,8 +41,10 @@ class Graph:
         self._runs = 0
         self._updates = 0
         self.flow_id = flow_id
-        self._inputs = []
-        self._outputs = []
+        self._is_input_vertices = []
+        self._is_output_vertices = []
+        self._has_session_id_vertices = []
+        self._sorted_vertices_layers = []
 
         self.top_level_vertices = []
         for vertex in self._vertices:
@@ -54,38 +57,37 @@ class Graph:
         self.inactive_vertices = set()
         self._build_graph()
         self.build_graph_maps()
-        self.define_inputs_and_outputs()
+        self.define_vertices_lists()
 
-    def define_inputs_and_outputs(self):
+    @property
+    def sorted_vertices_layers(self):
+        if not self._sorted_vertices_layers:
+            self.sort_vertices()
+        return self._sorted_vertices_layers
+
+    def define_vertices_lists(self):
         """
-        Defines the input and output vertices of the graph.
+        Defines the lists of vertices that are inputs, outputs, and have session_id.
         """
+        attributes = ["is_input", "is_output", "has_session_id"]
         for vertex in self.vertices:
-            if vertex.is_input:
-                self._inputs.append(vertex.id)
-            if vertex.is_output:
-                self._outputs.append(vertex.id)
+            for attribute in attributes:
+                if getattr(vertex, attribute):
+                    getattr(self, f"_{attribute}_vertices").append(vertex.id)
 
-    def run(self, inputs: Dict[str, str]) -> List["ResultData"]:
+    async def _run(self, inputs: Dict[str, str]) -> List["ResultData"]:
         """Runs the graph with the given inputs."""
-
-        # inputs is {"message": "Hello, world!"}
-        # we need to go through self.inputs and update the self._raw_params
-        # of the vertices that are inputs
-
         for vertex_id in self.inputs:
             vertex = self.get_vertex(vertex_id)
             if vertex is None:
                 raise ValueError(f"Vertex {vertex_id} not found")
             vertex.update_raw_params(inputs)
         try:
-            self.build()
+            await self.process()
             self.increment_run_count()
         except Exception as exc:
             logger.exception(exc)
             raise ValueError(f"Error running graph: {exc}") from exc
-
-        # Now we get the outputs from the self.outputs
         outputs = []
         for vertex_id in self.outputs:
             vertex = self.get_vertex(vertex_id)
@@ -94,6 +96,23 @@ class Graph:
             outputs.append(vertex.result)
         return outputs
 
+    async def run(self, inputs: Dict[str, Union[str, list[str]]]) -> List["ResultData"]:
+        """Runs the graph with the given inputs."""
+
+        # inputs is {"message": "Hello, world!"}
+        # we need to go through self.inputs and update the self._raw_params
+        # of the vertices that are inputs
+        # if the value is a list, we need to run multiple times
+        outputs = []
+        inputs_values = inputs.get("input_value")
+        if not isinstance(inputs_values, list):
+            inputs_values = [inputs_values]
+        for input_value in inputs_values:
+            run_outputs = await self._run({"input_value": input_value})
+            logger.debug(f"Run outputs: {run_outputs}")
+            outputs.extend(run_outputs)
+        return outputs
+
     @property
     def metadata(self):
         return {
@@ -404,6 +423,36 @@ class Graph:
             raise ValueError("No root vertex found")
         return await root_vertex.build()
 
+    async def process(self) -> "Graph":
+        """Processes the graph with vertices in each layer run in parallel."""
+        vertices_layers = self.sorted_vertices_layers
+
+        for layer_index, layer in enumerate(vertices_layers):
+            tasks = []
+            for vertex_id in layer:
+                vertex = self.get_vertex(vertex_id)
+                task = asyncio.create_task(
+                    vertex.build(), name=f"layer-{layer_index}-vertex-{vertex_id}"
+                )
+                tasks.append(task)
+            logger.debug(f"Running layer {layer_index} with {len(tasks)} tasks")
+            await self._execute_tasks(tasks)
+        logger.debug("Graph processing complete")
+        return self
+
+    async def _execute_tasks(self, tasks):
+        """Executes tasks in parallel, handling exceptions for each task."""
+        results = []
+        for task in asyncio.as_completed(tasks):
+            try:
+                result = await task
+                results.append(result)
+            except Exception as e:
+                # Log the exception along with the task name for easier debugging
+                task_name = task.get_name()
+                logger.error(f"Task {task_name} failed with exception: {e}")
+        return results
+
     def topological_sort(self) -> List[Vertex]:
         """
         Performs a topological sort of the vertices in the graph.
@@ -671,6 +720,7 @@ class Graph:
         vertices_layers = self.sort_by_avg_build_time(vertices_layers)
         vertices_layers = self.sort_chat_inputs_first(vertices_layers)
         self.increment_run_count()
+        self._sorted_vertices_layers = vertices_layers
         return vertices_layers
 
     def sort_interface_components_first(