directedGraph.addEdge(N1, N2, E12);
    directedGraph.addEdge(N1, N2, E12_A);
    directedGraph.addEdge(N1, N1, E11);
    directedGraph.addEdge(N3, N4, E34);

    MutableNetwork<Integer, String> expectedTranspose =
        NetworkBuilder.directed().allowsParallelEdges(true).allowsSelfLoops(true).build();
    expectedTranspose.addEdge(N3, N1, E13);
    expectedTranspose.addEdge(N1, N3, E31);
    expectedTranspose.addEdge(N2, N1, E12);

      network.addEdge(1, 2, "1-2a");
      network.addEdge(1, 2, "1-2b");
    }
    assertThat(hasCycle(directedNetwork)).isFalse();
    assertThat(hasCycle(undirectedNetwork)).isTrue(); // cyclic in undirected case
  }

  @Test
  public void hasCycle_cyclicMultigraph() {
    for (MutableNetwork<Integer, String> network : networksToTest) {
      network.addEdge(1, 2, "1-2a");

  }

  @Test
  public void edgesConnecting_directed() {
    MutableNetwork<String, String> mutableNetwork =
        NetworkBuilder.directed().allowsSelfLoops(true).build();
    mutableNetwork.addEdge("A", "A", "AA");
    mutableNetwork.addEdge("A", "B", "AB");
    Network<String, String> network = ImmutableNetwork.copyOf(mutableNetwork);

    assertThat(network.edgesConnecting("A", "A")).containsExactly("AA");

 * flightNetwork.addEdge("LAX", "ATL", 3025);
 * flightNetwork.addEdge("LAX", "ATL", 1598);
 * flightNetwork.addEdge("ATL", "LAX", 2450);
 *
 * // Building a immutable network
 * ImmutableNetwork<String, Integer> immutableNetwork =
 *     NetworkBuilder.directed()
 *         .allowsParallelEdges(true)
 *         .<String, Integer>immutable()
 *         .addEdge("LAX", "ATL", 3025)

 * @deprecated use {@code org.apache.maven.api.services.ModelBuilder} instead
 */
@Deprecated(since = "4.0.0")
class Graph {

    final Map<String, Set<String>> graph = new LinkedHashMap<>();

    synchronized void addEdge(String from, String to) throws CycleDetectedException {
        if (graph.computeIfAbsent(from, l -> new HashSet<>()).add(to)) {

   * @throws IllegalArgumentException if the introduction of the edge would violate {@link
   *     #allowsParallelEdges()} or {@link #allowsSelfLoops()}
   */
  @CanIgnoreReturnValue
  boolean addEdge(N nodeU, N nodeV, E edge);

  /**
   * Adds {@code edge} connecting {@code endpoints}. In an undirected network, {@code edge} will
   * also connect {@code nodeV} to {@code nodeU}.
   *

    public Collection<Vertex> getVertices() {
        return vertices.values();
    }

    Vertex addVertex(String label) {
        return vertices.computeIfAbsent(label, Vertex::new);
    }

    void addEdge(Vertex from, Vertex to) throws CycleDetectedException {
        from.children.add(to);
        to.parents.add(from);
        List<String> cycle = findCycle(to);
        if (cycle != null) {

    public Collection<Vertex> getVertices() {
        return vertices.values();
    }

    Vertex addVertex(String label) {
        return vertices.computeIfAbsent(label, Vertex::new);
    }

    void addEdge(Vertex from, Vertex to) throws CycleDetectedException {
        from.children.add(to);
        to.parents.add(from);
        List<String> cycle = findCycle(to);
        if (cycle != null) {

        {
            ArtifactMetadata md = node.getMd();
            MetadataGraphEdge e =
                    new MetadataGraphEdge(md.version, md.resolved, md.artifactScope, md.artifactUri, depth, pomOrder);
            addEdge(parentVertex, vertex, e);
        } else {
            entry = vertex;
        }

        MetadataTreeNode[] kids = node.getChildren();
        if (kids == null || kids.length < 1) {
            return;

    edgeToReferenceNode.put(edge, nodeU);
    return true;
  }

  @Override
  @CanIgnoreReturnValue
  public boolean addEdge(EndpointPair<N> endpoints, E edge) {
    validateEndpoints(endpoints);
    return addEdge(endpoints.nodeU(), endpoints.nodeV(), edge);
  }

  @Override
  @CanIgnoreReturnValue
  public boolean removeNode(N node) {
    checkNotNull(node, "node");