* Using DoubleUtils.bigToDouble, getting a double approximation of x is extremely fast, and
     * then we can get a double approximation of the square root. Then, we iteratively improve this
     * guess with an application of Newton's method, which sets guess := (guess + (x / guess)) / 2.
     * This iteration has the following two properties:
     *
     * a) every iteration (except potentially the first) has guess >= floor(sqrt(x)). This is

 * of the {@code Immutable*} types</a> for more information on the properties and guarantees
 * provided by this class.
 *
 * @author James Sexton
 * @author Joshua O'Madadhain
 * @author Omar Darwish
 * @author Jens Nyman
 * @param <N> Node parameter type
 * @since 20.0
 */
@Beta
@Immutable(containerOf = {"N"})
@ElementTypesAreNonnullByDefault

 *         .putEdgeValue("San Jose", "San Jose", 0.0)
 *         .putEdgeValue("San Francisco", "San Jose", 48.4)
 *         .build();
 * }</pre>
 *
 * @author James Sexton
 * @author Joshua O'Madadhain
 * @param <N> The most general node type this builder will support. This is normally {@code Object}
 *     unless it is constrained by using a method like {@link #nodeOrder}, or the builder is

 * of the {@code Immutable*} types</a> for more information on the properties and guarantees
 * provided by this class.
 *
 * @author James Sexton
 * @author Joshua O'Madadhain
 * @author Omar Darwish
 * @author Jens Nyman
 * @param <N> Node parameter type
 * @param <E> Edge parameter type
 * @since 20.0
 */
@Beta
@Immutable(containerOf = {"N", "E"})

import java.util.Set;
import java.util.concurrent.atomic.AtomicBoolean;
import javax.annotation.CheckForNull;

/**
 * An implementation of {@link GraphConnections} for directed graphs.
 *
 * @author James Sexton
 * @author Jens Nyman
 * @param <N> Node parameter type
 * @param <V> Value parameter type
 */
@ElementTypesAreNonnullByDefault
final class DirectedGraphConnections<N, V> implements GraphConnections<N, V> {
  /**

        AvlNode<E> newTop = pred();
        // newTop is the maximum node in my left subtree
        newTop.left = left.removeMax(newTop);
        newTop.right = right;
        newTop.distinctElements = distinctElements - 1;
        newTop.totalCount = totalCount - oldElemCount;
        return newTop.rebalance();
      } else {
        AvlNode<E> newTop = succ();

 *       Synchronization policy</a>
 *   <li><a href="https://github.com/google/guava/wiki/GraphsExplained#notes-for-implementors">Notes
 *       for implementors</a>
 * </ul>
 *
 * @author James Sexton
 * @author Joshua O'Madadhain
 * @param <N> Node parameter type
 * @param <V> Value parameter type
 * @since 20.0
 */
@Beta
@ElementTypesAreNonnullByDefault

import java.util.Collections;
import java.util.Map;
import java.util.Set;

/**
 * An implementation of {@link NetworkConnections} for undirected networks.
 *
 * @author James Sexton
 * @param <N> Node parameter type
 * @param <E> Edge parameter type
 */
@ElementTypesAreNonnullByDefault
final class UndirectedNetworkConnections<N, E> extends AbstractUndirectedNetworkConnections<N, E> {

import java.util.LinkedHashMap;
import java.util.Map;
import java.util.Set;
import javax.annotation.CheckForNull;

/**
 * An implementation of {@link GraphConnections} for undirected graphs.
 *
 * @author James Sexton
 * @param <N> Node parameter type
 * @param <V> Value parameter type
 */
@ElementTypesAreNonnullByDefault
final class UndirectedGraphConnections<N, V> implements GraphConnections<N, V> {

 *
 * <p>Time complexities for mutation methods are all O(1) except for {@code removeNode(N node)},
 * which is in O(d_node) where d_node is the degree of {@code node}.
 *
 * @author James Sexton
 * @author Joshua O'Madadhain
 * @author Omar Darwish
 * @param <N> Node parameter type
 * @param <V> Value parameter type
 */
@ElementTypesAreNonnullByDefault