* graph.putEdge("bread", "bread");
 * graph.putEdge("chocolate", "peanut butter");
 * graph.putEdge("peanut butter", "jelly");
 *
 * // Building an immutable graph
 * ImmutableGraph<String> immutableGraph =
 *     GraphBuilder.undirected()
 *         .allowsSelfLoops(true)
 *         .<String>immutable()
 *         .putEdge("bread", "bread")
 *         .putEdge("chocolate", "peanut butter")

      ValueGraphBuilder.directed().allowsSelfLoops(true).expectedNodeCount(16);

  private static final ImmutableGraph<String> IMMUTABLE_GRAPH_A =
      GraphBuilder.directed().<String>immutable().addNode("A").build();
  private static final ImmutableGraph<String> IMMUTABLE_GRAPH_B =
      GraphBuilder.directed().<String>immutable().addNode("B").build();

      ValueGraphBuilder.directed().allowsSelfLoops(true).expectedNodeCount(16);

  private static final ImmutableGraph<String> IMMUTABLE_GRAPH_A =
      GraphBuilder.directed().<String>immutable().addNode("A").build();
  private static final ImmutableGraph<String> IMMUTABLE_GRAPH_B =
      GraphBuilder.directed().<String>immutable().addNode("B").build();

 * you should use the non-mutating {@link Graph} interface, or an {@link ImmutableGraph}.
 *
 * <p>You can create an immutable copy of an existing {@code Graph} using {@link
 * ImmutableGraph#copyOf(Graph)}:
 *
 * <pre>{@code
 * ImmutableGraph<Integer> immutableGraph = ImmutableGraph.copyOf(graph);
 * }</pre>
 *
 * <p>Instances of {@link ImmutableGraph} do not implement {@link MutableGraph} (obviously!) and are

   *
   * @since 33.1.0 (present with return type {@code Graph} since 20.0)
   */
  // TODO(b/31438252): Consider potential optimizations for this algorithm.
  public static <N> ImmutableGraph<N> transitiveClosure(Graph<N> graph) {
    ImmutableGraph.Builder<N> transitiveClosure =
        GraphBuilder.from(graph).allowsSelfLoops(true).<N>immutable();
    // Every node is, at a minimum, reachable from itself. Since the resulting transitive closure

 * graph.putEdgeValue("San Jose", "San Jose", 0.0);
 * graph.putEdgeValue("San Francisco", "San Jose", 48.4);
 *
 * // Building an immutable value graph
 * ImmutableValueGraph<String, Double> immutableGraph =
 *     ValueGraphBuilder.undirected()
 *         .allowsSelfLoops(true)
 *         .<String, Double>immutable()
 *         .putEdgeValue("San Francisco", "San Francisco", 0.0)

    validateGraph(graph);
  }

  static <N> void validateGraph(Graph<N> graph) {
    assertStronglyEquivalent(graph, Graphs.copyOf(graph));
    assertStronglyEquivalent(graph, ImmutableGraph.copyOf(graph));

    String graphString = graph.toString();
    assertThat(graphString).contains("isDirected: " + graph.isDirected());
    assertThat(graphString).contains("allowsSelfLoops: " + graph.allowsSelfLoops());

    validateGraph(graph);
  }

  static <N> void validateGraph(Graph<N> graph) {
    assertStronglyEquivalent(graph, Graphs.copyOf(graph));
    assertStronglyEquivalent(graph, ImmutableGraph.copyOf(graph));

    String graphString = graph.toString();
    assertThat(graphString).contains("isDirected: " + graph.isDirected());
    assertThat(graphString).contains("allowsSelfLoops: " + graph.allowsSelfLoops());

 * ImmutableValueGraph}.
 *
 * <p>You can create an immutable copy of an existing {@code ValueGraph} using {@link
 * ImmutableValueGraph#copyOf(ValueGraph)}:
 *
 * <pre>{@code
 * ImmutableValueGraph<Integer, Double> immutableGraph = ImmutableValueGraph.copyOf(graph);
 * }</pre>
 *
 * <p>Instances of {@link ImmutableValueGraph} do not implement {@link MutableValueGraph}
 * (obviously!) and are contractually guaranteed to be unmodifiable and thread-safe.

        return Ordering.natural().immutableSortedCopy(graphMap.get(node));
      }
    };
  }

  private static ImmutableGraph<Character> createSingleRootGraph() {
    MutableGraph<Character> graph = GraphBuilder.directed().build();
    graph.addNode('a');
    return ImmutableGraph.copyOf(graph);
  }

  private static void assertEqualCharNodes(Iterable<Character> result, String expectedCharacters) {