// But in gcd(a - b, b), a - b is even and b is odd, so we can divide out powers of two.

      // We bend over backwards to avoid branching, adapting a technique from
      // http://graphics.stanford.edu/~seander/bithacks.html#IntegerMinOrMax

      long delta = a - b; // can't overflow, since a and b are nonnegative

      long minDeltaOrZero = delta & (delta >> (Long.SIZE - 1));

 * Static utility methods for {@link Graph}, {@link ValueGraph}, and {@link Network} instances.
 *
 * @author James Sexton
 * @author Joshua O'Madadhain
 * @since 20.0
 */
public final class Graphs extends GraphsBridgeMethods {

  private Graphs() {}

  // Graph query methods

  /**
   * Returns true if {@code graph} has at least one cycle. A cycle is defined as a non-empty subset

   * multiple graphs in series. Each new graph contains all the elements of the ones created before
   * it.
   *
   * @since 28.0
   */
  public static class Builder<N, V> {

    private final MutableValueGraph<N, V> mutableValueGraph;

    Builder(ValueGraphBuilder<N, V> graphBuilder) {
      // The incidentEdgeOrder for immutable graphs is always stable. However, we don't want to

   * multiple graphs in series. Each new graph contains all the elements of the ones created before
   * it.
   *
   * @since 28.0
   */
  public static class Builder<N> {

    private final MutableGraph<N> mutableGraph;

    Builder(GraphBuilder<N> graphBuilder) {
      // The incidentEdgeOrder for immutable graphs is always stable. However, we don't want to

  @Nullable Integer expectedNodeCount = null;

  /**
   * Creates a new instance with the specified edge directionality.
   *
   * @param directed if true, creates an instance for graphs whose edges are each directed; if
   *     false, creates an instance for graphs whose edges are each undirected.
   */
  AbstractGraphBuilder(boolean directed) {
    this.directed = directed;
  }

  private GraphBuilder(boolean directed) {
    super(directed);
  }

  /** Returns a {@link GraphBuilder} for building directed graphs. */
  public static GraphBuilder<Object> directed() {
    return new GraphBuilder<>(true);
  }

  /** Returns a {@link GraphBuilder} for building undirected graphs. */
  public static GraphBuilder<Object> undirected() {
    return new GraphBuilder<>(false);
  }

  /**

    super(directed);
  }

  /** Returns a {@link ValueGraphBuilder} for building directed graphs. */
  public static ValueGraphBuilder<Object, Object> directed() {
    return new ValueGraphBuilder<>(true);
  }

  /** Returns a {@link ValueGraphBuilder} for building undirected graphs. */
  public static ValueGraphBuilder<Object, Object> undirected() {
    return new ValueGraphBuilder<>(false);
  }

  /**

 * href="https://github.com/google/guava/wiki/GraphsExplained#definitions">definitions of
 * terms</a>):
 *
 * <ul>
 *   <li>directed graphs
 *   <li>undirected graphs
 *   <li>graphs that do/don't allow self-loops
 *   <li>graphs whose nodes/edges are insertion-ordered, sorted, or unordered
 *   <li>graphs whose edges have associated values
 * </ul>
 *

import java.util.Set;

/**
 * Supertype for {@link Graphs}, containing the old signatures of methods whose signatures we've
 * changed. This provides binary compatibility for users who compiled against the old signatures.
 */
abstract class GraphsBridgeMethods {

  @SuppressWarnings("PreferredInterfaceType")
  public static <N> Graph<N> transitiveClosure(Graph<N> graph) {
    return Graphs.transitiveClosure(graph);
  }

 * href="https://github.com/google/guava/wiki/GraphsExplained#definitions">definitions of
 * terms</a>):
 *
 * <ul>
 *   <li>directed graphs
 *   <li>undirected graphs
 *   <li>graphs that do/don't allow self-loops
 *   <li>graphs whose nodes/edges are insertion-ordered, sorted, or unordered
 * </ul>
 *
 * <p>{@code Graph} explicitly does not support parallel edges, and forbids implementations or