*
 * <p>The {@link #outEdgeToNode} map allows this class to work on networks with parallel edges. See
 * {@link EdgesConnecting} for a class that is more efficient but forbids parallel edges.
 *
 * @author James Sexton
 * @param <E> Edge parameter type
 */
@ElementTypesAreNonnullByDefault
abstract class MultiEdgesConnecting<E> extends AbstractSet<E> {

  private final Map<E, ?> outEdgeToNode;
  private final Object targetNode;

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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> {

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

/**
 * An interface for representing and manipulating an origin node's adjacent nodes and incident edges
 * in a {@link Network}.
 *
 * @author James Sexton
 * @param <N> Node parameter type
 * @param <E> Edge parameter type
 */
@ElementTypesAreNonnullByDefault
interface NetworkConnections<N, E> {

  Set<N> adjacentNodes();

  Set<N> predecessors();

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

/**
 * A base implementation of {@link NetworkConnections} for directed networks.
 *
 * @author James Sexton
 * @param <N> Node parameter type
 * @param <E> Edge parameter type
 */
@ElementTypesAreNonnullByDefault
abstract class AbstractDirectedNetworkConnections<N, E> implements NetworkConnections<N, E> {

import java.util.Set;
import javax.annotation.CheckForNull;
import org.checkerframework.checker.nullness.qual.Nullable;

/**
 * A class to facilitate the set returned by {@link Graph#edges()}.
 *
 * @author James Sexton
 */
@ElementTypesAreNonnullByDefault
abstract class EndpointPairIterator<N> extends AbstractIterator<EndpointPair<N>> {
  private final BaseGraph<N> graph;
  private final Iterator<N> nodeIterator;

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

/**
 * An implementation of {@link NetworkConnections} for undirected networks with parallel edges.
 *
 * @author James Sexton
 * @param <N> Node parameter type
 * @param <E> Edge parameter type
 */
@ElementTypesAreNonnullByDefault
final class UndirectedMultiNetworkConnections<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> {

import javax.annotation.CheckForNull;

/**
 * A subinterface of {@link ValueGraph} which adds mutation methods. When mutation is not required,
 * users should prefer the {@link ValueGraph} interface.
 *
 * @author James Sexton
 * @param <N> Node parameter type
 * @param <V> Value parameter type
 * @since 20.0
 */
@Beta
@ElementTypesAreNonnullByDefault
public interface MutableValueGraph<N, V> extends ValueGraph<N, V> {

  /**

 * this class rather than implement {@link ValueGraph} directly.
 *
 * <p>The methods implemented in this class should not be overridden unless the subclass admits a
 * more efficient implementation.
 *
 * @author James Sexton
 * @param <N> Node parameter type
 * @param <V> Value parameter type
 * @since 20.0
 */
@Beta
@ElementTypesAreNonnullByDefault
public abstract class AbstractValueGraph<N, V> extends AbstractBaseGraph<N>