<< (*graph)->num_edges();
        is_module_updated = true;
      }
    } else if (pass_state == MlirOptimizationPassState::FallbackEnabled) {
      VLOG(2) << "Run MLIR graph optimization pass with fallback: "
              << StringRefToView(name);
      VLOG(2) << "Graph #nodes " << (*graph)->num_nodes() << " #edges "
              << (*graph)->num_edges();

/**
 * Standard implementation of {@link Network} that supports the options supplied by {@link
 * NetworkBuilder}.
 *
 * <p>This class maintains a map of nodes to {@link NetworkConnections}. This class also maintains a
 * map of edges to reference nodes. The reference node is defined to be the edge's source node on
 * directed graphs, and an arbitrary endpoint of the edge on undirected graphs.
 *

/**
 * Standard implementation of {@link Network} that supports the options supplied by {@link
 * NetworkBuilder}.
 *
 * <p>This class maintains a map of nodes to {@link NetworkConnections}. This class also maintains a
 * map of edges to reference nodes. The reference node is defined to be the edge's source node on
 * directed graphs, and an arbitrary endpoint of the edge on undirected graphs.
 *

			M[obj] = &graphNode{obj: obj}
		}
	}

	// compute edges for graph M
	// (We need to include all nodes, even isolated ones, because they still need
	// to be scheduled for initialization in correct order relative to other nodes.)
	for obj, n := range M {
		// for each dependency obj -> d (= deps[i]), create graph edges n->s and s->n
		for d := range objMap[obj].deps {

			M[obj] = &graphNode{obj: obj}
		}
	}

	// compute edges for graph M
	// (We need to include all nodes, even isolated ones, because they still need
	// to be scheduled for initialization in correct order relative to other nodes.)
	for obj, n := range M {
		// for each dependency obj -> d (= deps[i]), create graph edges n->s and s->n
		for d := range objMap[obj].deps {

    auto const& pair = visited.insert(nout.node());
    if (pair.second) {
      queue.push_back(std::make_pair(nout.node(), static_cast<Node*>(nullptr)));
    }
  }
  // BFS from nodes in 'inputs_' along out edges for the entire graph. Internal
  // output nodes are recorded during the traversal. All nodes that are output
  // nodes but not internal output nodes are considered the frontier of the

  ASSERT_EQ(f1_rewritten->signature().output_arg_size(), 1);
  EXPECT_EQ(f1_rewritten->signature().output_arg(0).type(), DT_BOOL);

  // Check node "if" input and output edges.
  auto node_name_index = g->BuildNodeNameIndex();
  const Node *if_node = node_name_index.at("if");
  ASSERT_NE(if_node, nullptr);
  const Node *input_node;
  TF_CHECK_OK(if_node->input_node(1, &input_node));

  // We need to introduce this version to adapt to the output of gpu inference
  // converter. The single argument overload version calls this function.
  //
  // When add_edges_to_output_of_downstream_nodes is true, the output edges of
  // the xla_launch_node's immediate downstream nodes would be attached to the
  // generated xla node. For example, if the original graph is
  // StatefulPartitionedCall{_xla_compile_id=1} -> XlaClusterOutput -> NodeA

// and transforms the module in place to cluster the given ops for compilation
// that is compatible with the given device_type. The MLIR should be in the TF
// Executor Dialect for graph nodes and edges or be in TF Functional already.
// Individual Op inside a node should be the Tensorflow Functional Dialect. The
// output MLIR is in the TF Functional Dialect. Returns OkStatus if passed,
// otherwise an error.
//
// Inputs:

	{"tighten tuple selectors", "schedule"},
	// remove critical edges before phi tighten, so that phi args get better placement
	{"critical", "phi tighten"},
	// don't layout blocks until critical edges have been removed
	{"critical", "layout"},
	// regalloc requires the removal of all critical edges
	{"critical", "regalloc"},
	// regalloc requires all the values in a block to be scheduled