core[patch]: Fixed trim functions, and added corresponding unit test for the solved issue (#28429)

- **Description:** 
- Trim functions were incorrectly deleting nodes with more than 1
outgoing/incoming edge, so an extra condition was added to check for
this directly. A unit test "test_trim_multi_edge" was written to test
this test case specifically.
- **Issue:** 
  - Fixes #28411 
  - Fixes https://github.com/langchain-ai/langgraph/issues/1676
- **Dependencies:** 
  - No changes were made to the dependencies

- [x] Unit tests were added to verify the changes.
- [x] Updated documentation where necessary.
- [x] Ran make format, make lint, and make test to ensure compliance
with project standards.

---------

Co-authored-by: Tasif Hussain <tasif006@gmail.com>

libs/core/langchain_core/runnables/graph.py

@@ -470,14 +470,22 @@ class Graph:
         """Remove the first node if it exists and has a single outgoing edge,
         i.e., if removing it would not leave the graph without a "first" node."""
         first_node = self.first_node()
-        if first_node and _first_node(self, exclude=[first_node.id]):
+        if (
+            first_node
+            and _first_node(self, exclude=[first_node.id])
+            and len({e for e in self.edges if e.source == first_node.id}) == 1
+        ):
             self.remove_node(first_node)
 
     def trim_last_node(self) -> None:
         """Remove the last node if it exists and has a single incoming edge,
         i.e., if removing it would not leave the graph without a "last" node."""
         last_node = self.last_node()
-        if last_node and _last_node(self, exclude=[last_node.id]):
+        if (
+            last_node
+            and _last_node(self, exclude=[last_node.id])
+            and len({e for e in self.edges if e.target == last_node.id}) == 1
+        ):
             self.remove_node(last_node)
 
     def draw_ascii(self) -> str:

libs/core/tests/unit_tests/runnables/test_graph.py

@@ -69,6 +69,26 @@ def test_trim(snapshot: SnapshotAssertion) -> None:
     assert graph.last_node() is end
 
 
+def test_trim_multi_edge() -> None:
+    class Scheme(BaseModel):
+        a: str
+
+    graph = Graph()
+    start = graph.add_node(Scheme, id="__start__")
+    a = graph.add_node(Scheme, id="a")
+    last = graph.add_node(Scheme, id="__end__")
+
+    graph.add_edge(start, a)
+    graph.add_edge(a, last)
+    graph.add_edge(start, last)
+
+    graph.trim_first_node()  # should not remove __start__ since it has 2 outgoing edges
+    assert graph.first_node() is start
+
+    graph.trim_last_node()  # should not remove the __end__ node since it has 2 incoming edges
+    assert graph.last_node() is last
+
+
 def test_graph_sequence(snapshot: SnapshotAssertion) -> None:
     fake_llm = FakeListLLM(responses=["a"])
     prompt = PromptTemplate.from_template("Hello, {name}!")