assertNotNull(res.getExcidentEdges(v1), "no edges in the resulting graph after resolver");

        assertEquals(4, res.getVertices().size(), "wrong # of vertices in the resulting graph after resolver");
        assertEquals(
                2,
                res.getExcidentEdges(v1).size(),
                "wrong # of excident edges in the resulting graph entry after resolver");

        assertEquals(

		return math.NaN(), false
	}

	// Sort edges.
	edges := d.unsorted
	slices.SortFunc(edges, func(a, b edge) int {
		return cmp.Compare(a.x, b.x)
	})
	// Merge with sorted edges.
	d.unsorted = nil
	if d.sorted == nil {
		d.sorted = edges
	} else {
		oldSorted := d.sorted
		newSorted := make([]edge, len(oldSorted)+len(edges))
		i, j := 0, 0
		for o := range newSorted {

	g.edges[from][to] = true
}

func (g *Graph) DelEdge(from, to string) {
	delete(g.edges[from], to)
}

func (g *Graph) HasEdge(from, to string) bool {
	return g.edges[from] != nil && g.edges[from][to]
}

func (g *Graph) Edges(from string) []string {
	edges := make([]string, 0, 16)
	for k := range g.edges[from] {
		edges = append(edges, k)
	}
	slices.SortFunc(edges, func(a, b string) int {

			b.Values = append(b.Values, v)

			// Find all the scheduling edges out from this value.
			i := sort.Search(len(edges), func(i int) bool {
				return edges[i].x.ID >= v.ID
			})
			j := sort.Search(len(edges), func(i int) bool {
				return edges[i].x.ID > v.ID
			})
			// Decrement inEdges for each target of edges from v.
			for _, e := range edges[i:j] {
				inEdges[e.y.ID]--
				if inEdges[e.y.ID] == 0 {

        // If none of the incoming edges are transitive, remove previous state and do not traverse.
        // If not traversed before, simply add all selected outgoing edges (either hard or pending edges)
        // If traversed before:
        //      If net exclusions for this node have not changed, ignore
        //      If net exclusions for this node have changed, remove previous state and traverse outgoing edges again.

}

// edgeEntropyScore computes the entropy value for a set of edges
// coming in or out of a node. Entropy (as defined in information
// theory) refers to the amount of information encoded by the set of
// edges. A set of edges that have a more interesting distribution of
// samples gets a higher score.
func edgeEntropyScore(n *Node, edges EdgeMap, self int64) float64 {
	score := float64(0)
	total := self

		var b bytes.Buffer
		g.TransitiveReduction()
		// Add cyclic edges for visualization.
		for k := range cyclicRanks {
			g.AddEdge(k, k)
		}
		// Reverse the graph. It's much easier to read this as
		// a "<" partial order than a ">" partial order. This
		// ways, locks are acquired from the top going down
		// and time moves forward over the edges instead of
		// backward.
		g.Transpose()
		generateDot(&b, g)

        // the following only needs to be done serially to preserve ordering of dependencies in the graph: we have visited the edges
        // but we still didn't add the result to the queue. Doing it from resolve threads would result in non-reproducible graphs, where
        // edges could be added in different order. To avoid this, the addition of new edges is done serially.
        for (EdgeState dependency : dependencies) {

  graph_->AddEdge(input_node_it->second, 0, dst_node, dst_index);
  return absl::OkStatus();
}

Status Exporter::AddEdge(Operation* inst) {
  // For tf_executor.fetch, add only its data edges. Control edges are captured
  // later.
  if (auto fetch = llvm::dyn_cast<mlir::tf_executor::FetchOp>(inst)) {
    for (auto operand_and_idx : llvm::enumerate(fetch.getOperands())) {
      Value operand = operand_and_idx.value();

  graph_->AddEdge(input_node_it->second, 0, dst_node, dst_index);
  return absl::OkStatus();
}

Status Exporter::AddEdge(Operation* inst) {
  // For tf_executor.fetch, add only its data edges. Control edges are captured
  // later.
  if (auto fetch = llvm::dyn_cast<mlir::tf_executor::FetchOp>(inst)) {
    for (auto operand_and_idx : llvm::enumerate(fetch.getOperands())) {
      Value operand = operand_and_idx.value();