template<typename G>
struct Graph {
  /**
   * The size_type of a graph is an integral type that can encode the largest
   * possible number of edges admissable by the graph type. Note that the
   * number of edges in even a simple graph can be O(|V|^2), which is why the
   * Graph's size type is determined by edge count rather than vertex count.
   */
  typedef ... size_type;

  /** \brief Returns the number of vertices in a graph.
   * The order of a graph is determined by the number of vertices. A graph with
   * whose order is 0 is said to be a null graph.
   */
  size_type order() const;

  /** \brief Returns true if the graph has no vertices.
   * A graph with no vertices (i.e., of order 0) is said to be a null graph. A
   * null graph has no edges.
   */
  bool null() const;

  /** @brief Returns the number of edges in a graph.
   * The size of a graph is determined by the number of edges connecting its
   * verticse. A graph with no edges is said to be empty.
   */
  size_type size() const;

  /** @brief Returns true if the graph has no edges.
   * A graph with no edges (i.e., of size 0) is said to be an empty graph. Note
   * that all null graphs are also empty.
   */
  bool empty() const;
};