diff --git a/libs/core/langchain_core/runnables/graph.py b/libs/core/langchain_core/runnables/graph.py
index 4f35205e853..bb4559f35a2 100644
--- a/libs/core/langchain_core/runnables/graph.py
+++ b/libs/core/langchain_core/runnables/graph.py
@@ -11,6 +11,7 @@ from typing import (
     List,
     NamedTuple,
     Optional,
+    Protocol,
     Tuple,
     Type,
     TypedDict,
@@ -25,6 +26,11 @@ if TYPE_CHECKING:
     from langchain_core.runnables.base import Runnable as RunnableType
 
 
+class Stringifiable(Protocol):
+    def __str__(self) -> str:
+        ...
+
+
 class LabelsDict(TypedDict):
     """Dictionary of labels for nodes and edges in a graph."""
 
@@ -55,7 +61,7 @@ class Edge(NamedTuple):
 
     source: str
     target: str
-    data: Optional[str] = None
+    data: Optional[Stringifiable] = None
     conditional: bool = False
 
 
@@ -253,7 +259,7 @@ class Graph:
         self,
         source: Node,
         target: Node,
-        data: Optional[str] = None,
+        data: Optional[Stringifiable] = None,
         conditional: bool = False,
     ) -> Edge:
         """Add an edge to the graph and return it."""
diff --git a/libs/core/langchain_core/runnables/graph_mermaid.py b/libs/core/langchain_core/runnables/graph_mermaid.py
index b99c90f9a70..402b0ee4f31 100644
--- a/libs/core/langchain_core/runnables/graph_mermaid.py
+++ b/libs/core/langchain_core/runnables/graph_mermaid.py
@@ -81,7 +81,7 @@ def draw_mermaid(
         # Add BR every wrap_label_n_words words
         if edge.data is not None:
             edge_data = edge.data
-            words = edge_data.split()  # Split the string into words
+            words = str(edge_data).split()  # Split the string into words
             # Group words into chunks of wrap_label_n_words size
             if len(words) > wrap_label_n_words:
                 edge_data = "<br>".join(
diff --git a/libs/core/langchain_core/runnables/graph_png.py b/libs/core/langchain_core/runnables/graph_png.py
index 75983ad279c..0fbeec7e354 100644
--- a/libs/core/langchain_core/runnables/graph_png.py
+++ b/libs/core/langchain_core/runnables/graph_png.py
@@ -160,8 +160,8 @@ class PngDrawer:
             self.add_node(viz, node)
 
     def add_edges(self, viz: Any, graph: Graph) -> None:
-        for start, end, label, cond in graph.edges:
-            self.add_edge(viz, start, end, label, cond)
+        for start, end, data, cond in graph.edges:
+            self.add_edge(viz, start, end, str(data), cond)
 
     def update_styles(self, viz: Any, graph: Graph) -> None:
         if first := graph.first_node():