Add pre-commit check for invalid build graph state (#5658)

This can catch things like dependency cycles introduced by
`fix-cc-deps`.

scripts/check_build_graph.py

@@ -0,0 +1,23 @@
+#!/usr/bin/env python3
+
+"""Verify that the bazel build graph is in a valid state, for pre-commit."""
+
+__copyright__ = """
+Part of the Carbon Language project, under the Apache License v2.0 with LLVM
+Exceptions. See /LICENSE for license information.
+SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+"""
+
+import subprocess
+
+import scripts_utils
+
+
+def main() -> None:
+    scripts_utils.chdir_repo_root()
+    bazel = scripts_utils.locate_bazel()
+    subprocess.check_call([bazel, "build", "--nobuild", "//..."])
+
+
+if __name__ == "__main__":
+    main()