IncidenceGraph

The IncidenceGraph concept provides an interface for efficient access to the out-edges of each vertex in the graph.

Refinement of

Notation

`G`	A type that is a model of IncidenceGraph.
`g`	An object of type `G`.
`e`	An object of type `boost::graph_traits<G>::edge_descriptor`.
`u, v`	Are objects of type `boost::graph_traits<G>::vertex_descriptor`.

Associated Types

boost::graph_traits<G>::traversal_category

This tag type must be convertible to incidence_graph_tag.

boost::graph_traits<G>::out_edge_iterator

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

boost::graph_traits<G>::degree_size_type

The unsigned intergral type used for representing the number out-edges or incident edges of a vertex.

Valid Expressions

`source(e, g)`	Returns the vertex descriptor for u of the edge (u,v) represented by `e`. Return type: `vertex_descriptor`
`target(e, g)`	Returns the vertex descriptor for v of the edge (u,v) represented by `e`. Return type: `vertex_descriptor`
`out_edges(u, g)`	Returns an iterator-range providing access to the out-edges (for directed graphs) or incident edges (for undirected graphs) of vertex `u` in graph `g`. The source vertex of an edge obtained via an out edge iterator is guaranteed (for both directed and undirected graphs) to be the vertex `u` used in the call to `out_edges(u, g)` and the target vertex must the a vertex adjacent to `u`.[1] Return type: `std::pair<out_edge_iterator, out_edge_iterator>`
`out_degree(u, g)`	Returns the number of out-edges (for directed graphs) or the number of incident edges (for undirected graphs) of vertex `u` in graph `g`. Return type: `degree_size_type`

Complexity guarantees

The source(), target(), and out_edges() functions must all be constant time. The out_degree() function must be linear in the number of out-edges.

Notes

[1] For undirected graphs, the edge (u,v) is the same as edge (v,u), so without some extra guarantee an implementation would be free use any ordering for the pair of vertices in an out-edge. For example, if you call out_edges(u, g), and v is one of the vertices adjacent to u, then the implementation would be free to return (v,u) as an out-edge which would be non-intuitive and cause trouble for algorithms. Therefore, the extra requirement is added that the out-edge connecting u and v must be given as (u,v) and not (v,u).

Concept Checking Class

  template <class G>
  struct IncidenceGraphConcept
  {
    typedef typename boost::graph_traits<G>::out_edge_iterator out_edge_iterator;
    void constraints() {
      function_requires< GraphConcept<G> >();
      function_requires< MultiPassInputIteratorConcept<out_edge_iterator> >();

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

Jeremy Siek, Indiana University ([email protected])
Lie-Quan Lee, Indiana University ([email protected])
Andrew Lumsdaine, Indiana University ([email protected])