}

  private static SuccessorsFunction<Character> createDirectedGraph(String... edges) {
    return createGraph(/* directed= */ true, edges);
  }

  private static SuccessorsFunction<Character> createUndirectedGraph(String... edges) {
    return createGraph(/* directed= */ false, edges);
  }

  /**

  // Check for undeclared outputs before Encapsulation, so we can give a better
  // error message.
  // TODO(phawkins): merge this with the encapsulation code to avoid the extra
  // O(n) pass over the edges.
  for (const Edge* e : (*graph)->edges()) {
    if (!e->IsControlEdge() &&
        e->src()->attrs().Find(kXlaClusterIdAttr) != nullptr &&
        e->dst()->attrs().Find(kXlaClusterIdAttr) == nullptr &&

        }

        private visitEdges(NodeBuilder node, Set<NodeBuilder> seenNodes, Set<EdgeBuilder> edges) {
            for (EdgeBuilder edge : node.deps) {
                edges.add(edge)
                if (seenNodes.add(edge.selected)) {
                    visitEdges(edge.selected, seenNodes, edges)
                }
            }
        }

        /**

                << (*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();

 *       locks---to each of the acquired locks, an edge from the soon-to-be-acquired lock is either
 *       verified or created.
 *   <li>If a new edge needs to be created, the outgoing edges of the acquired locks are traversed
 *       to check for a cycle that reaches the lock to be acquired. If no cycle is detected, a new
 *       "safe" edge is created.

			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

        return current;
    }

    private Collection<DependencyEdge> toDependencyEdges(Collection<DependencyResult> dependencies) {
        List<DependencyEdge> edges = CollectionUtils.collect(dependencies, TO_EDGES);
        return DependencyResultSorter.sort(edges, versionSelectorScheme, versionComparator, versionParser);
    }

  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));