diff --git a/langgraph/constants.py b/langgraph/constants.py
index c43b3174f..41970ae16 100644
--- a/langgraph/constants.py
+++ b/langgraph/constants.py
@@ -7,6 +7,9 @@ TASKS = "__pregel_tasks"
 RESERVED = {INTERRUPT, TASKS, CONFIG_KEY_SEND, CONFIG_KEY_READ}
 TAG_HIDDEN = "langsmith:hidden"
 
+START = "__start__"
+END = "__end__"
+
 
 class Send:
     """A message or packet to send to a specific node in the graph.
diff --git a/langgraph/graph/graph.py b/langgraph/graph/graph.py
index 7c91901c4..6a1fa8ff6 100644
--- a/langgraph/graph/graph.py
+++ b/langgraph/graph/graph.py
@@ -26,7 +26,7 @@ from langchain_core.runnables.graph import (
 
 from langgraph.channels.ephemeral_value import EphemeralValue
 from langgraph.checkpoint import BaseCheckpointSaver
-from langgraph.constants import TAG_HIDDEN, Send
+from langgraph.constants import END, START, TAG_HIDDEN, Send
 from langgraph.errors import InvalidUpdateError
 from langgraph.pregel import Channel, Pregel
 from langgraph.pregel.read import PregelNode
@@ -36,9 +36,6 @@ from langgraph.utils import DrawableGraph, RunnableCallable, coerce_to_runnable
 
 logger = logging.getLogger(__name__)
 
-START = "__start__"
-END = "__end__"
-
 
 class Branch(NamedTuple):
     path: Runnable[Any, Union[str, list[str]]]
@@ -341,10 +338,11 @@ class Graph:
 
         # validate the graph
         self.validate(
-            interrupt=(interrupt_before if interrupt_before != "*" else [])
-            + interrupt_after
-            if interrupt_after != "*"
-            else []
+            interrupt=(
+                (interrupt_before if interrupt_before != "*" else []) + interrupt_after
+                if interrupt_after != "*"
+                else []
+            )
         )
 
         # create empty compiled graph
@@ -404,9 +402,11 @@ class CompiledGraph(Pregel):
     def attach_branch(self, start: str, name: str, branch: Branch) -> None:
         def branch_writer(packets: list[Union[str, Send]]) -> Optional[ChannelWrite]:
             writes = [
-                ChannelWriteEntry(f"branch:{start}:{name}:{p}" if p != END else END)
-                if not isinstance(p, Send)
-                else p
+                (
+                    ChannelWriteEntry(f"branch:{start}:{name}:{p}" if p != END else END)
+                    if not isinstance(p, Send)
+                    else p
+                )
                 for p in packets
             ]
             return ChannelWrite(writes, tags=[TAG_HIDDEN])