}

  @Override
  public Set<E> edgesConnecting(N nodeU, N nodeV) {
    Set<E> outEdgesU = outEdges(nodeU);
    Set<E> inEdgesV = inEdges(nodeV);
    return nodePairInvalidatableSet(
        outEdgesU.size() <= inEdgesV.size()
            ? unmodifiableSet(Sets.filter(outEdgesU, connectedPredicate(nodeU, nodeV)))
            : unmodifiableSet(Sets.filter(inEdgesV, connectedPredicate(nodeV, nodeU))),

    if (!allowsSelfLoops && nodeU == nodeV) { // just an optimization, only check reference equality
      return ImmutableSet.of();
    }
    checkArgument(containsNode(nodeV), NODE_NOT_IN_GRAPH, nodeV);
    return nodePairInvalidatableSet(connectionsU.edgesConnecting(nodeV), nodeU, nodeV);
  }

  @Override
  public Set<E> inEdges(N node) {
    return nodeInvalidatableSet(checkedConnections(node).inEdges(), node);
  }

  @Override