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);

    // for ug1, add e12 first, then e12_a
    g1.addEdge(N1, N2, E12);
    g1.addEdge(N1, N2, E12_A);

    // for ug2, add e12_a first, then e12
    g2.addEdge(N1, N2, E12_A);
    g2.addEdge(N1, N2, E12);

    assertThat(g1).isEqualTo(g2);
  }

  @Test
  public void equivalent_edgeDirectionsDiffer() {
    network.addEdge(N1, N2, E12);

    // for ug1, add e12 first, then e12_a
    g1.addEdge(N1, N2, E12);
    g1.addEdge(N1, N2, E12_A);

    // for ug2, add e12_a first, then e12
    g2.addEdge(N1, N2, E12_A);
    g2.addEdge(N1, N2, E12);

    assertThat(g1).isEqualTo(g2);
  }

  @Test
  public void equivalent_edgeDirectionsDiffer() {
    network.addEdge(N1, N2, E12);

        // v1-->v2
        graph.addEdge(v1, v2, new MetadataGraphEdge("1.1", true, null, null, 2, 1));
        graph.addEdge(v1, v2, new MetadataGraphEdge("1.2", true, null, null, 2, 2));

        // v1-->v3
        graph.addEdge(v1, v3, new MetadataGraphEdge("1.1", true, null, null, 2, 1));
        graph.addEdge(v1, v3, new MetadataGraphEdge("1.2", true, null, null, 4, 2));

        // v3-->v4

public class GraphTest {

    @Test
    void testCycle() throws Graph.CycleDetectedException {
        Graph graph = new Graph();
        graph.addEdge("a1", "a2");
        assertThrows(Graph.CycleDetectedException.class, () -> graph.addEdge("a2", "a1"));
    }

    @Test
    public void testPerf() throws IOException {
        List<String[]> data = new ArrayList<>();
        String k = null;

    return networkBuilder.build();
  }

  @Override
  void addNode(Integer n) {
    networkBuilder.addNode(n);
    network = networkBuilder.build();
  }

  @Override
  void addEdge(Integer n1, Integer n2, String e) {
    networkBuilder.addEdge(n1, n2, e);
    network = networkBuilder.build();
  }

      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");

      ArrayList<Integer> nodeList = new ArrayList<>(network.nodes());
      for (int i = 0; i < NUM_EDGES; ++i) {
        // Parallel edges are allowed, so this should always succeed.
        assertThat(
                network.addEdge(
                    getRandomElement(nodeList, gen), getRandomElement(nodeList, gen), new Object()))
            .isTrue();
      }
      ArrayList<Object> edgeList = new ArrayList<>(network.edges());

 * 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)