Bidirectional

BidirectionalGraph

The BidirectionalGraph concept refines IncidenceGraph and adds the requirement for efficient access to the in-edges of each vertex. This concept is separated from IncidenceGraph because for directed graphs efficient access to in-edges typically requires more storage space, and many algorithms do not require access to in-edges. For undirected graphs this is not an issue, since the in_edges() and out_edges() functions are the same, they both return the edges incident to the vertex.

Refinement of

IncidenceGraph

Notation

`G`	A type that is a model of Graph.
`g`	An object of type `G`.
`v`	An object of type `boost::graph_traits<G>::vertex_descriptor`.

Associated Types

boost::graph_traits<G>::traversal_category

This tag type must be convertible to bidirectional_graph_tag.

boost::graph_traits<G>::in_edge_iterator

An in-edge iterator for a vertex v provides access to the in-edges of v. As such, the value type of an in-edge iterator is the edge descriptor type of its graph. An in-edge iterator must meet the requirements of MultiPassInputIterator.

Valid Expressions

`in_edges(v, g)`	Returns an iterator-range providing access to the in-edges (for directed graphs) or incident edges (for undirected graphs) of vertex `v` in graph `g`. For both directed and undirected graphs, the target of an out-edge is required to be vertex `v` and the source is required to be a vertex that is adjacent to `v`. Return type: `std::pair<in_edge_iterator, in_edge_iterator>`
`in_degree(v, g)`	Returns the number of in-edges (for directed graphs) or the number of incident edges (for undirected graphs) of vertex `v` in graph `g`. Return type: `degree_size_type`
`degree(v, g)`	Returns the number of in-edges plus out-edges (for directed graphs) or the number of incident edges (for undirected graphs) of vertex `v` in graph `g`. Return type: `degree_size_type`

Models

adjacency_list with Directed=bidirectionalS
adjacency_list with Directed=undirectedS

Complexity guarantees

The in_edges() function is required to be constant time. The in_degree() and degree() functions must be linear in the number of in-edges (for directed graphs) or incident edges (for undirected graphs).

Concept Checking Class

  template <class G>
  struct BidirectionalGraphConcept
  {
    typedef typename boost::graph_traits<G>::in_edge_iterator
      in_edge_iterator;
    void constraints() {
      BOOST_CONCEPT_ASSERT(( IncidenceGraphConcept<G> ));
      BOOST_CONCEPT_ASSERT(( MultiPassInputIteratorConcept<in_edge_iterator> ));

      p = in_edges(v, g);
      e = *p.first;
      const_constraints(g);
    }
    void const_constraints(const G& g) {
      p = in_edges(v, g);
      e = *p.first;
    }
    std::pair<in_edge_iterator, in_edge_iterator> p;
    typename boost::graph_traits<G>::vertex_descriptor v;
    typename boost::graph_traits<G>::edge_descriptor e;
    G g;
  };

Jeremy Siek, Indiana University (jsiek@osl.iu.edu)