assertThat(e).hasMessageThat().contains(ERROR_PARALLEL_EDGE);
  }

  @Test
  public void addEdge_parallelEdge_allowsParallelEdges() {
    assume().that(graphIsMutable()).isTrue();
    assume().that(network.allowsParallelEdges()).isTrue();

    assertTrue(networkAsMutableNetwork.addEdge(N1, N2, E12));
    assertTrue(networkAsMutableNetwork.addEdge(N1, N2, E12_A));

  }

  @Test
  public void transpose_directedNetwork() {
    MutableNetwork<Integer, String> directedGraph =
        NetworkBuilder.directed().allowsParallelEdges(true).allowsSelfLoops(true).build();
    directedGraph.addEdge(N1, N3, E13);
    directedGraph.addEdge(N3, N1, E31);
    directedGraph.addEdge(N1, N2, E12);
    directedGraph.addEdge(N1, N2, E12_A);

    assertThat(e).hasMessageThat().contains(ERROR_PARALLEL_EDGE);
  }

  @Test
  public void addEdge_parallelEdge_allowsParallelEdges() {
    assume().that(graphIsMutable()).isTrue();
    assume().that(network.allowsParallelEdges()).isTrue();

    assertTrue(networkAsMutableNetwork.addEdge(N1, N2, E12));
    assertTrue(networkAsMutableNetwork.addEdge(N2, N1, E21));

    String networkString = network.toString();
    assertThat(networkString).contains("isDirected: " + network.isDirected());
    assertThat(networkString).contains("allowsParallelEdges: " + network.allowsParallelEdges());
    assertThat(networkString).contains("allowsSelfLoops: " + network.allowsSelfLoops());

    int nodeStart = networkString.indexOf("nodes:");
    int edgeStart = networkString.indexOf("edges:");

    String networkString = network.toString();
    assertThat(networkString).contains("isDirected: " + network.isDirected());
    assertThat(networkString).contains("allowsParallelEdges: " + network.allowsParallelEdges());
    assertThat(networkString).contains("allowsSelfLoops: " + network.allowsSelfLoops());

    int nodeStart = networkString.indexOf("nodes:");
    int edgeStart = networkString.indexOf("edges:");

    assertThat(e).hasMessageThat().contains(ERROR_PARALLEL_EDGE);
  }

  @Test
  public void addEdge_parallelEdge_allowsParallelEdges() {
    assume().that(graphIsMutable()).isTrue();
    assume().that(network.allowsParallelEdges()).isTrue();

    assertTrue(networkAsMutableNetwork.addEdge(N1, N2, E12));
    assertTrue(networkAsMutableNetwork.addEdge(N2, N1, E21));

    assertThat(e).hasMessageThat().contains(ERROR_PARALLEL_EDGE);
  }

  @Test
  public void addEdge_parallelEdge_allowsParallelEdges() {
    assume().that(graphIsMutable()).isTrue();
    assume().that(network.allowsParallelEdges()).isTrue();

    assertTrue(networkAsMutableNetwork.addEdge(N1, N2, E12));
    assertTrue(networkAsMutableNetwork.addEdge(N1, N2, E12_A));

  }

  @Test
  public void transpose_directedNetwork() {
    MutableNetwork<Integer, String> directedGraph =
        NetworkBuilder.directed().allowsParallelEdges(true).allowsSelfLoops(true).build();
    directedGraph.addEdge(N1, N3, E13);
    directedGraph.addEdge(N3, N1, E31);
    directedGraph.addEdge(N1, N2, E12);
    directedGraph.addEdge(N1, N2, E12_A);

  }

  /** Returns a string representation of this network. */
  @Override
  public String toString() {
    return "isDirected: "
        + isDirected()
        + ", allowsParallelEdges: "
        + allowsParallelEdges()
        + ", allowsSelfLoops: "
        + allowsSelfLoops()
        + ", nodes: "
        + nodes()
        + ", edges: "
        + edgeIncidentNodesMap(this);
  }

  /**

   * an edge connecting node A to node B if this {@link Network} has an edge connecting A to B.
   *
   * <p>If this network {@link #allowsParallelEdges() allows parallel edges}, parallel edges will be
   * treated as if collapsed into a single edge. For example, the {@link #degree(Object)} of a node