graph: improve generics on StateGraph etc + move typing utils to private file (#4982)

docs/docs/concepts/low_level.md

@@ -89,7 +89,7 @@ def node_3(state: PrivateState) -> OutputState:
     # Read from PrivateState, write to OutputState
     return {"graph_output": state["bar"] + " Lance"}
 
-builder = StateGraph(OverallState,input=InputState,output=OutputState)
+builder = StateGraph(OverallState,input_schema=InputState,output_schema=OutputState)
 builder.add_node("node_1", node_1)
 builder.add_node("node_2", node_2)
 builder.add_node("node_3", node_3)
@@ -107,7 +107,7 @@ There are two subtle and important points to note here:
 
 1. We pass `state: InputState` as the input schema to `node_1`. But, we write out to `foo`, a channel in `OverallState`. How can we write out to a state channel that is not included in the input schema? This is because a node _can write to any state channel in the graph state._ The graph state is the union of the state channels defined at initialization, which includes `OverallState` and the filters `InputState` and `OutputState`.
 
-2. We initialize the graph with `StateGraph(OverallState,input=InputState,output=OutputState)`. So, how can we write to `PrivateState` in `node_2`? How does the graph gain access to this schema if it was not passed in the `StateGraph` initialization? We can do this because _nodes can also declare additional state channels_ as long as the state schema definition exists. In this case, the `PrivateState` schema is defined, so we can add `bar` as a new state channel in the graph and write to it.
+2. We initialize the graph with `StateGraph(OverallState,input_schema=InputState,output_schema=OutputState)`. So, how can we write to `PrivateState` in `node_2`? How does the graph gain access to this schema if it was not passed in the `StateGraph` initialization? We can do this because _nodes can also declare additional state channels_ as long as the state schema definition exists. In this case, the `PrivateState` schema is defined, so we can add `bar` as a new state channel in the graph and write to it.
 
 ### Reducers
 

docs/docs/concepts/server-mcp.md

@@ -94,7 +94,7 @@ def answer_node(state: InputState):
     return {"answer": "bye", "question": state["question"]}
 
 # Build the graph with explicit schemas
-builder = StateGraph(OverallState, input=InputState, output=OutputState)
+builder = StateGraph(OverallState, input_schema=InputState, output_schema=OutputState)
 builder.add_node(answer_node)
 builder.add_edge(START, "answer_node")
 builder.add_edge("answer_node", END)

docs/docs/how-tos/graph-api.ipynb

@@ -439,7 +439,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": null,
    "id": "6ec0eb77-874e-443e-8c73-93125b515106",
    "metadata": {},
    "outputs": [
@@ -478,7 +478,7 @@
     "\n",
     "\n",
     "# Build the graph with input and output schemas specified\n",
-    "builder = StateGraph(OverallState, input=InputState, output=OutputState)\n",
+    "builder = StateGraph(OverallState, input_schema=InputState, output_schema=OutputState)\n",
     "builder.add_node(answer_node)  # Add the answer node\n",
     "builder.add_edge(START, \"answer_node\")  # Define the starting edge\n",
     "builder.add_edge(\"answer_node\", END)  # Define the ending edge\n",
@@ -3430,7 +3430,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.9"
+   "version": "3.9.6"
   }
  },
  "nbformat": 4,