for (E edge : sanityCheckSet(network.edges())) {
      // TODO(b/27817069): Consider verifying the edge's incident nodes in the string.
      assertThat(edgeString).contains(edge.toString());

      EndpointPair<N> endpointPair = network.incidentNodes(edge);
      N nodeU = endpointPair.nodeU();
      N nodeV = endpointPair.nodeV();
      assertThat(asGraph.edges()).contains(EndpointPair.of(network, nodeU, nodeV));

   *
   * <p>In the undirected case, returns {@code null} if {@code isSelfLoop} is true.
   */
  @CanIgnoreReturnValue
  @Nullable N removeInEdge(E edge, boolean isSelfLoop);

  /** Remove {@code edge} from the set of outgoing edges. Returns the former successor node. */
  @CanIgnoreReturnValue
  N removeOutEdge(E edge);

  /**

    private MetadataGraphEdge cleanEdges(
            MetadataGraphVertex v, List<MetadataGraphEdge> edges, ArtifactScopeEnum scope) {
        if (edges == null || edges.isEmpty()) {
            return null;
        }

        if (edges.size() == 1) {
            MetadataGraphEdge e = edges.get(0);
            if (scope.encloses(e.getScope())) {
                return e;
            }

    for (N node : graph.nodes()) {
      copy.addNode(node);
    }
    for (EndpointPair<N> edge : graph.edges()) {
      copy.putEdge(edge.nodeU(), edge.nodeV());
    }
    return copy;
  }

  /** Creates a mutable copy of {@code graph} with the same nodes, edges, and edge values. */
  public static <N, V> MutableValueGraph<N, V> copyOf(ValueGraph<N, V> graph) {
    MutableValueGraph<N, V> copy =

    for (N node : graph.nodes()) {
      copy.addNode(node);
    }
    for (EndpointPair<N> edge : graph.edges()) {
      copy.putEdge(edge.nodeU(), edge.nodeV());
    }
    return copy;
  }

  /** Creates a mutable copy of {@code graph} with the same nodes, edges, and edge values. */
  public static <N, V> MutableValueGraph<N, V> copyOf(ValueGraph<N, V> graph) {
    MutableValueGraph<N, V> copy =

    ImmutableSet<String> edges = ImmutableSet.copyOf(network.edges());
    assertThat(networkAsMutableNetwork.addEdge(N1, N2, E12)).isFalse();
    assertThat(network.edges()).containsExactlyElementsIn(edges);
    assertThat(networkAsMutableNetwork.addEdge(N2, N1, E12)).isFalse();
    assertThat(network.edges()).containsExactlyElementsIn(edges);
  }

  @Test

 *       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.
 *   <li>If a cycle is detected, an "unsafe" (cyclic) edge is created to represent a potential

public interface SuccessorsFunction<N> {

  /**
   * Returns all nodes in this graph adjacent to {@code node} which can be reached by traversing
   * {@code node}'s outgoing edges in the direction (if any) of the edge.
   *
   * <p>This is <i>not</i> the same as "all nodes reachable from {@code node} by following outgoing

        + nodes()
        + ", edges: "
        + edgeValueMap(this);
  }

  private static <N, V> Map<EndpointPair<N>, V> edgeValueMap(ValueGraph<N, V> graph) {
    return Maps.asMap(
        graph.edges(),
        edge ->
            // requireNonNull is safe because the endpoint pair comes from the graph.
            requireNonNull(graph.edgeValueOrDefault(edge.nodeU(), edge.nodeV(), null)));
  }

    assertThat(network.edgeOrder())
        .isEqualTo(ElementOrder.sorted(Ordering.<String>natural().reverse()));
    assertThat(network.edges()).containsExactly("p", "i", "e").inOrder();
    assertThat(network.nodeOrder()).isEqualTo(ElementOrder.insertion()); // default
  }

  // Combined node and edge order tests

  @Test
  public void nodeOrderUnorderedAndEdgesSorted() {
    MutableNetwork<Integer, String> network =