diff --git a/lightrag/base.py b/lightrag/base.py
index 1d7a0a98..3d4fc022 100644
--- a/lightrag/base.py
+++ b/lightrag/base.py
@@ -163,17 +163,13 @@ class BaseGraphStorage(StorageNameSpace):
     """Get an edge by its source and target node ids."""
 
     async def get_edge(
-        self, 
-        source_node_id: str, 
-        target_node_id: str
-    ) -> dict[str, str] | None :
+        self, source_node_id: str, target_node_id: str
+    ) -> dict[str, str] | None:
         raise NotImplementedError
 
     """Get all edges connected to a node."""
 
-    async def get_node_edges(
-        self, source_node_id: str
-    ) -> list[tuple[str, str]] | None:
+    async def get_node_edges(self, source_node_id: str) -> list[tuple[str, str]] | None:
         raise NotImplementedError
 
     """Upsert a node into the graph."""
diff --git a/lightrag/types.py b/lightrag/types.py
index 2510bed3..40e61bc4 100644
--- a/lightrag/types.py
+++ b/lightrag/types.py
@@ -1,4 +1,3 @@
-
 from __future__ import annotations
 
 from pydantic import BaseModel
diff --git a/lightrag/utils.py b/lightrag/utils.py
index 5b86ee78..c8786e7b 100644
--- a/lightrag/utils.py
+++ b/lightrag/utils.py
@@ -488,7 +488,7 @@ def cosine_similarity(v1, v2):
     return dot_product / (norm1 * norm2)
 
 
-def quantize_embedding(embedding: np.ndarray | list[float], bits: int=8) -> tuple:
+def quantize_embedding(embedding: np.ndarray | list[float], bits: int = 8) -> tuple:
     """Quantize embedding to specified bits"""
     # Convert list to numpy array if needed
     if isinstance(embedding, list):