return nodeInvalidatableSet(checkedConnections(node).incidentEdges(), node);
  }

  @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

        return Ints.saturatedCast(edgeCount());
      }

      @Override
      public boolean remove(@CheckForNull Object o) {
        throw new UnsupportedOperationException();
      }

      // Mostly safe: We check contains(u) before calling successors(u), so we perform unsafe
      // operations only in weird cases like checking for an EndpointPair<ArrayList> in a
      // Graph<LinkedList>.
      @SuppressWarnings("unchecked")

    return nodeInvalidatableSet(checkedConnections(node).incidentEdges(), node);
  }

  @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

         *            sqrtFloor^2 <= x < (sqrtFloor + 1)^2
         * halfSquare - sqrtFloor <= x < halfSquare + sqrtFloor + 1
         * so |x - halfSquare| <= sqrtFloor.  Therefore, it's safe to treat x - halfSquare as a
         * signed long, so lessThanBranchFree is safe for use.
         */
        return sqrtFloor + lessThanBranchFree(halfSquare, x);
    }
    throw new AssertionError();
  }

  /**

      implied, including, without limitation, any warranties or conditions
      of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
      PARTICULAR PURPOSE. You are solely responsible for determining the
      appropriateness of using or redistributing the Work and assume any
      risks associated with Your exercise of permissions under this License.

      implied, including, without limitation, any warranties or conditions
      of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
      PARTICULAR PURPOSE. You are solely responsible for determining the
      appropriateness of using or redistributing the Work and assume any
      risks associated with Your exercise of permissions under this License.

      implied, including, without limitation, any warranties or conditions
      of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
      PARTICULAR PURPOSE. You are solely responsible for determining the
      appropriateness of using or redistributing the Work and assume any
      risks associated with Your exercise of permissions under this License.

      implied, including, without limitation, any warranties or conditions
      of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
      PARTICULAR PURPOSE. You are solely responsible for determining the
      appropriateness of using or redistributing the Work and assume any
      risks associated with Your exercise of permissions under this License.

      implied, including, without limitation, any warranties or conditions
      of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
      PARTICULAR PURPOSE. You are solely responsible for determining the
      appropriateness of using or redistributing the Work and assume any
      risks associated with Your exercise of permissions under this License.

      implied, including, without limitation, any warranties or conditions
      of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
      PARTICULAR PURPOSE. You are solely responsible for determining the
      appropriateness of using or redistributing the Work and assume any
      risks associated with Your exercise of permissions under this License.