assume().that(graphIsMutable()).isTrue();

    putEdge(N1, N2);
    putEdge(N1, N3);
    putEdge(N1, N4);
    assertThat(graphAsMutableGraph.removeEdge(N1, N3)).isTrue();
    assertThat(graph.adjacentNodes(N1)).containsExactly(N2, N4);
  }

  @Test
  public void removeEdge_nodeNotPresent() {
    assume().that(graphIsMutable()).isTrue();

    putEdge(N1, N2);

    undirectedGraph.putEdge(N2, N3);
    undirectedGraph.putEdge(N3, N4);

    MutableGraph<Integer> expectedClosure = GraphBuilder.undirected().allowsSelfLoops(true).build();
    expectedClosure.putEdge(N1, N1);
    expectedClosure.putEdge(N1, N2);
    expectedClosure.putEdge(N1, N3);
    expectedClosure.putEdge(N1, N4);
    expectedClosure.putEdge(N2, N2);
    expectedClosure.putEdge(N2, N3);
    expectedClosure.putEdge(N2, N4);

   * insertion order.
   */
  private void populateStarShapedGraph() {
    putEdge(2, 1);
    putEdge(1, 4);
    putEdge(1, 3);
    putEdge(5, 1);
    putEdge(1, 2);
    putEdge(3, 1);
  }

  // Element Mutation

  @Test
  public void putEdge_existingNodes() {
    assume().that(graphIsMutable()).isTrue();

        .build();
  }

  @Override
  final void addNode(Integer n) {
    graphAsMutableGraph.addNode(n);
  }

  @Override
  final void putEdge(Integer n1, Integer n2) {
    graphAsMutableGraph.putEdge(n1, n2);
  }

    g1.putEdge(N1, N2);
    g1.putEdge(N3, N1);

    // for g2, add 3->1 first, then 1->2
    g2.putEdge(N3, N1);
    g2.putEdge(N1, N2);

    assertThat(g1).isEqualTo(g2);
  }

  @Test
  public void equivalent_edgeDirectionsDiffer() {
    graph.putEdge(N1, N2);

    MutableGraph<Integer> g2 = createGraph(edgeType);
    g2.putEdge(N2, N1);

    switch (edgeType) {

    MutableGraph<Integer> directedGraph = GraphBuilder.directed().allowsSelfLoops(true).build();
    directedGraph.addNode(N0);
    directedGraph.putEdge(N1, N2);
    directedGraph.putEdge(N2, N1);
    directedGraph.putEdge(N1, N3);
    directedGraph.putEdge(N4, N4);
    containsExactlySanityCheck(
        directedGraph.edges(),
        EndpointPair.ordered(N1, N2),
        EndpointPair.ordered(N2, N1),

    MutableGraph<Integer> directedGraph = GraphBuilder.directed().allowsSelfLoops(true).build();
    directedGraph.addNode(N0);
    directedGraph.putEdge(N1, N2);
    directedGraph.putEdge(N2, N1);
    directedGraph.putEdge(N1, N3);
    directedGraph.putEdge(N4, N4);
    containsExactlySanityCheck(
        directedGraph.edges(),
        EndpointPair.ordered(N1, N2),
        EndpointPair.ordered(N2, N1),

    assume().that(graphIsMutable()).isTrue();

    putEdge(N1, N2);
    putEdge(N1, N3);
    putEdge(N1, N4);
    assertThat(graphAsMutableGraph.removeEdge(N1, N3)).isTrue();
    assertThat(graph.adjacentNodes(N1)).containsExactly(N2, N4);
  }

  @Test
  public void removeEdge_nodeNotPresent() {
    assume().that(graphIsMutable()).isTrue();

    putEdge(N1, N2);

        graph.addNode(gen.nextInt(NODE_POOL_SIZE));
      }
      ArrayList<Integer> nodeList = new ArrayList<>(graph.nodes());
      while (graph.edges().size() < NUM_EDGES) {
        graph.putEdge(getRandomElement(nodeList, gen), getRandomElement(nodeList, gen));
      }
      ArrayList<EndpointPair<Integer>> edgeList = new ArrayList<>(graph.edges());

      assertThat(graph.nodes()).hasSize(NUM_NODES);

    return backingValueGraph.addNode(node);
  }

  @Override
  public boolean putEdge(N nodeU, N nodeV) {
    return backingValueGraph.putEdgeValue(nodeU, nodeV, Presence.EDGE_EXISTS) == null;
  }

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

  @Override
  public boolean removeNode(N node) {