* user-defined properties.
 *
 * <p>A {@code Network} built by this class has the following default properties:
 *
 * <ul>
 *   <li>does not allow parallel edges
 *   <li>does not allow self-loops
 *   <li>orders {@link Network#nodes()} and {@link Network#edges()} in the order in which the
 *       elements were added (insertion order)
 * </ul>
 *

    int edgeStart = graphString.indexOf("edges:");
    String nodeString = graphString.substring(nodeStart, edgeStart);

    Network<N, EndpointPair<N>> asNetwork = graph.asNetwork();
    // Don't call AbstractNetworkTest.validateNetwork(asNetwork).  Mutual recursion.
    assertThat(graph.nodes()).isEqualTo(asNetwork.nodes());
    assertThat(graph.edges()).hasSize(asNetwork.edges().size());

  }

  @Override
  public EndpointPair<N> incidentNodes(E edge) {
    N nodeU = checkedReferenceNode(edge);
    // requireNonNull is safe because checkedReferenceNode made sure the edge is in the network.
    N nodeV = requireNonNull(nodeConnections.get(nodeU)).adjacentNode(edge);
    return EndpointPair.of(this, nodeU, nodeV);
  }

  @Override

  }

  @Override
  public EndpointPair<N> incidentNodes(E edge) {
    N nodeU = checkedReferenceNode(edge);
    // requireNonNull is safe because checkedReferenceNode made sure the edge is in the network.
    N nodeV = requireNonNull(nodeConnections.get(nodeU)).adjacentNode(edge);
    return EndpointPair.of(this, nodeU, nodeV);
  }

  @Override

 */
@Beta
@DoNotMock("Implement with a lambda, or use GraphBuilder to build a Graph with the desired edges")
public interface PredecessorsFunction<N> {

  /**
   * Returns all nodes in this graph adjacent to {@code node} which can be reached by traversing
   * {@code node}'s incoming edges <i>against</i> the direction (if any) of the edge.
   *
   * <p>Some algorithms that operate on a {@code PredecessorsFunction} may produce undesired results

    public Builder<N> addNode(N node) {
      mutableGraph.addNode(node);
      return this;
    }

    /**
     * Adds an edge connecting {@code nodeU} to {@code nodeV} if one is not already present.
     *
     * <p>If the graph is directed, the resultant edge will be directed; otherwise, it will be
     * undirected.
     *

    // Thus we avoid modifying the underlying view while iterating over it.
    for (E edge : ImmutableList.copyOf(connections.incidentEdges())) {
      removeEdge(edge);
    }
    nodeConnections.remove(node);
    return true;
  }

  @Override
  @CanIgnoreReturnValue
  public boolean removeEdge(E edge) {
    checkNotNull(edge, "edge");

    N nodeU = edgeToReferenceNode.get(edge);

                    PluginExecution existing = merged.get(key);
                    if (existing != null) {
                        mergePluginExecution(existing, element, sourceDominant, context);
                    } else {
                        merged.put(key, element.clone());
                    }
                }

                target.setExecutions(new ArrayList<>(merged.values()));
            }
        }

      mutableValueGraph.addNode(node);
      return this;
    }

    /**
     * Adds an edge connecting {@code nodeU} to {@code nodeV} if one is not already present, and
     * sets a value for that edge to {@code value} (overwriting the existing value, if any).
     *
     * <p>If the graph is directed, the resultant edge will be directed; otherwise, it will be
     * undirected.
     *

   *     #allowsParallelEdges()} or {@link #allowsSelfLoops()}
   */
  @CanIgnoreReturnValue
  boolean addEdge(N nodeU, N nodeV, E edge);

  /**
   * Adds {@code edge} connecting {@code endpoints}. In an undirected network, {@code edge} will
   * also connect {@code nodeV} to {@code nodeU}.
   *