@Test
  public void edgesConnecting_parallelEdges() {
    network.addEdge(N1, N2, E12);
    network.addEdge(N1, N2, E12_A);
    network.addEdge(N2, N1, E21);
    if (edgeType == EdgeType.DIRECTED) {
      assertThat(networkForTest.edgesConnecting(N1, N2)).containsExactly(E12, E12_A);
      assertThat(networkForTest.edgesConnecting(N2, N1)).containsExactly(E21);
    } else {

 * 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)

    addEdge(N1, N1, E11);
    addEdge(N1, N2, E12);
    assertThat(network.adjacentEdges(E11)).containsExactly(E12);
  }

  @Test
  public void edgesConnecting_selfLoop() {
    assume().that(network.allowsSelfLoops()).isTrue();

    addEdge(N1, N1, E11);
    assertThat(network.edgesConnecting(N1, N1)).containsExactly(E11);
    addEdge(N1, N2, E12);

    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);

  }

  @Test
  public void adjacentEdges_bothEndpoints() {
    addEdge(N1, N2, E12);
    addEdge(N2, N3, E23);
    addEdge(N3, N1, E31);
    addEdge(N3, N4, E34);
    assertThat(network.adjacentEdges(E12)).containsExactly(E31, E23);
  }

  @Test
  public void adjacentEdges_noAdjacentEdges() {
    addEdge(N1, N2, E12);
    addEdge(N3, N4, E34);
    assertThat(network.adjacentEdges(E12)).isEmpty();
  }

  }

  @Test
  public void adjacentEdges_bothEndpoints() {
    addEdge(N1, N2, E12);
    addEdge(N2, N3, E23);
    addEdge(N3, N1, E31);
    addEdge(N3, N4, E34);
    assertThat(network.adjacentEdges(E12)).containsExactly(E31, E23);
  }

  @Test
  public void adjacentEdges_noAdjacentEdges() {
    addEdge(N1, N2, E12);
    addEdge(N3, N4, E34);
    assertThat(network.adjacentEdges(E12)).isEmpty();
  }

    // 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);

      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");

        // 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

  @Test
  public void edgesConnecting_parallelEdges() {
    network.addEdge(N1, N2, E12);
    network.addEdge(N1, N2, E12_A);
    network.addEdge(N2, N1, E21);
    if (edgeType == EdgeType.DIRECTED) {
      assertThat(networkForTest.edgesConnecting(N1, N2)).containsExactly(E12, E12_A);
      assertThat(networkForTest.edgesConnecting(N2, N1)).containsExactly(E21);
    } else {