public interface UndirectedGraph {

  /**
   * @return the number of vertices plus number of edges
   */
  public int size();

  /**
   * @return true iff the graph has no edges and no vertices
   */
  public boolean isEmpty();

  /**
   * @return the number of vertices
   */
  public int numVertices();

  /**
   * @return the number of edges
   */
  public int numEdges();

  /**
   * @return an enumeration over the vertices
   */
  public Enumeration vertices();

  /**
   * @return an enumeration over the edges
   */
  public Enumeration edges();

  /**
   * @param v a vertex
   * @return the number of (undirected) edges incident with v
   */
  public int degree (Vertex v) throws InvalidPositionException;

  /**
   * @param v a vertex
   * @return an enumeration over all vertices adjacent to v
   */
  public Enumeration adjacentVertices (Vertex v) throws
  InvalidPositionException;

  /**
   * @param v a vertex
   * @return an enumeration over all edges incident with v
   */
  public Enumeration incidentEdges (Vertex v) throws InvalidPositionException;

  /**
   * @param e an edge
   * @return an enumeration over the two endvertices of e
   */
  public Vertex[] endVertices (Edge e) throws InvalidPositionException;

  /**
   * @param e an edge
   * @param v one endvertex of e
   * @return the endvertex of e different from v
   * @throws InvalidEdgeException When v is not an endpoint of e
   */
  public Vertex opposite (Vertex v, Edge e) throws InvalidEdgeException,
    InvalidPositionException;

  /**
   * Inserts a new isolated vertex containing an object.
   * @param info the object to be stored in the new vertex
   * @return the new vertex
   */
  public Vertex insertVertex (Object info) throws InvalidPositionException;

  /**
   * Inserts a new undirected edge between two existing vertices.
   * @param u the first endvertex
   * @param v the second endvertex
   * @return the new edge
   */
  public Edge insertEdge (Vertex u, Vertex v, Object info)
     throws InvalidPositionException;

  /**
   * Deletes a vertex and all its incident edges.  If you need the locators
   * stored at the removed edges, get the locators beforehand.<p>
   * @param v the vertex to be deleted
   * @return Locator formerly stored at v
   */
  public Object removeVertex (Vertex v) throws InvalidPositionException;
  
  /**
   * Removes an edge.
   * @param e the edge to be removed
   * @return The removed edge's element
   */
  public Object removeEdge (Edge e) throws InvalidPositionException;
  
}