// gathered with problem collector
                }
                return null;
            }
        };
    }

    private boolean addEdge(Path from, Path p, DefaultModelProblemCollector problems) {
        try {
            dag.addEdge(from.toString(), p.toString());
            return true;
        } catch (Graph.CycleDetectedException e) {
            problems.add(new DefaultModelProblem(

    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);

    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);

    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);

        Graph.Vertex ep3 = graph.addVertex("$$$" + phase.name());
        graph.addEdge(ep0, ep1);
        graph.addEdge(ep1, ep2);
        graph.addEdge(ep2, ep3);
        if (before != null) {
            graph.addEdge(before, ep0);
        }
        if (after != null) {
            graph.addEdge(ep3, after);
        }
        phase.links().forEach(link -> {

  }

  @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();
  }

        // 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

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

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

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

  @Test

    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);