connections.removePredecessor(node);
        --edgeCount;
      }
    }

    for (N successor : ImmutableList.copyOf(connections.successors())) {
      // requireNonNull is safe because the node is a successor.
      requireNonNull(nodeConnections.getWithoutCaching(successor)).removePredecessor(node);
      requireNonNull(connections.removeSuccessor(successor));
      --edgeCount;
    }

        (nodeConnections instanceof TreeMap)
            ? new MapRetrievalCache<>(nodeConnections)
            : new MapIteratorCache<>(nodeConnections);
    this.edgeCount = checkNonNegative(edgeCount);
  }

  @Override
  public Set<N> nodes() {
    return nodeConnections.unmodifiableKeySet();
  }

  @Override
  public boolean isDirected() {
    return isDirected;
  }

  @Override

    return delegate().nodes();
  }

  /**
   * Defer to {@link AbstractGraph#edges()} (based on {@link #successors(Object)}) for full edges()
   * implementation.
   */
  @Override
  protected long edgeCount() {
    return delegate().edges().size();
  }

  @Override
  public boolean isDirected() {
    return delegate().isDirected();
  }

  @Override
  public boolean allowsSelfLoops() {

   * This implementation requires O(|N|) time. Classes extending this one may manually keep track of
   * the number of edges as the graph is updated, and override this method for better performance.
   */
  protected long edgeCount() {
    long degreeSum = 0L;
    for (N node : nodes()) {
      degreeSum += degree(node);
    }
    // According to the degree sum formula, this is equal to twice the number of edges.

  private static final String E31 = "3-1";
  private static final String E34 = "3-4";
  private static final String E44 = "4-4";
  private static final int NODE_COUNT = 20;
  private static final int EDGE_COUNT = 20;
  // TODO(user): Consider adding both error messages from here and {@link AbstractNetworkTest}
  // in one class (may be a utility class for error messages).