assertThat(e.getMessage()).contains(ERROR_PARALLEL_EDGE);
    e = assertThrows(IllegalArgumentException.class, () -> undirectedGraph.addEdge(N2, N1, E21));
    assertThat(e.getMessage()).contains(ERROR_PARALLEL_EDGE);

    // By default, self-loop edges are not allowed.
    e = assertThrows(IllegalArgumentException.class, () -> undirectedGraph.addEdge(N1, N1, E11));

          assertThat(graph.hasEdgeConnecting(endpoints.nodeU(), endpoints.nodeV())).isTrue();
        }
      }
    }

    sanityCheckSet(graph.edges());
    assertThat(graph.edges()).doesNotContain(EndpointPair.of(graph, new Object(), new Object()));
    assertThat(graph.edges()).isEqualTo(allEndpointPairs);
  }

  /**
   * Verifies that the {@code Set} returned by {@code nodes} has the expected mutability property

    assertThat(network.edgeOrder())
        .isEqualTo(ElementOrder.sorted(Ordering.<String>natural().reverse()));
    assertThat(network.edges()).containsExactly("p", "i", "e").inOrder();
    assertThat(network.nodeOrder()).isEqualTo(ElementOrder.insertion()); // default
  }

  // Combined node and edge order tests

  @Test
  public void nodeOrderUnorderedAndEdgesSorted() {
    MutableNetwork<Integer, String> network =

 */
@Beta
@DoNotMock("Implement with a lambda, or use GraphBuilder to build a Graph with the desired edges")
@ElementTypesAreNonnullByDefault
public interface SuccessorsFunction<N> {

  /**
   * Returns all nodes in this graph adjacent to {@code node} which can be reached by traversing
   * {@code node}'s outgoing edges in the direction (if any) of the edge.
   *

@Beta
@DoNotMock("Implement with a lambda, or use GraphBuilder to build a Graph with the desired edges")
@ElementTypesAreNonnullByDefault
public interface PredecessorsFunction<N> {

  /**
   * Returns all nodes in this graph adjacent to {@code node} which can be reached by traversing
   * {@code node}'s incoming edges <i>against</i> the direction (if any) of the edge.
   *

   *       <ul>
   *         <li>{@code edges()}: Stable order
   *         <li>{@code adjacentNodes(node)}: Connecting edge insertion order
   *         <li>{@code predecessors(node)}: Connecting edge insertion order
   *         <li>{@code successors(node)}: Connecting edge insertion order
   *         <li>{@code incidentEdges(node)}: Edge insertion order
   *       </ul>
   *   <li>For {@link Network}:

        while (resultWithDoubleSelfLoop.hasNext()) {
          EndpointPair<N> edge = resultWithDoubleSelfLoop.next();
          if (edge.nodeU().equals(edge.nodeV())) {
            if (!alreadySeenSelfLoop.getAndSet(true)) {
              return edge;
            }
          } else {
            return edge;
          }
        }
        return endOfData();
      }
    };
  }

    public Builder<N> addNode(N node) {
      mutableGraph.addNode(node);
      return this;
    }

    /**
     * Adds an edge connecting {@code nodeU} to {@code nodeV} if one is not already present.
     *
     * <p>If the graph is directed, the resultant edge will be directed; otherwise, it will be
     * undirected.
     *

  }

  @Override
  public N adjacentNode(E edge) {
    // Since the reference node is defined to be 'source' for directed graphs,
    // we can assume this edge lives in the set of outgoing edges.
    // (We're relying on callers to call this method only with an edge that's in the graph.)
    return requireNonNull(outEdgeMap.get(edge));
  }

  @Override
  public N removeInEdge(E edge, boolean isSelfLoop) {
    if (isSelfLoop) {

    ValueGraphBuilder<N1, V1> castBuilder = cast();
    return new ImmutableValueGraph.Builder<>(castBuilder);
  }

  /**
   * Specifies whether the graph will allow self-loops (edges that connect a node to itself).
   * Attempting to add a self-loop to a graph that does not allow them will throw an {@link
   * UnsupportedOperationException}.
   *
   * <p>The default value is {@code false}.
   */