Modified form of "example/bfs-example.cpp" code (https://github.com/boostorg/graph/blob/master/example/bfs-example.cpp) showing BFS with visitors

Boost_Reference_Manual_Page_169_code.cpp

#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/breadth_first_search.hpp>
#include <boost/pending/indirect_cmp.hpp>
#include <boost/range/irange.hpp>

#include <iostream>

template < typename TimeMap > class bfs_time_visitor:public boost::default_bfs_visitor {
  typedef typename boost::property_traits < TimeMap >::value_type T;
public:
  bfs_time_visitor(TimeMap tmap, T & t):m_timemap(tmap), m_time(t) { }
  template < typename Vertex, typename Graph >
    void discover_vertex(Vertex u, const Graph & g) const
  {
    put(m_timemap, u, m_time++);
  }
  TimeMap m_timemap;
  T & m_time;
};


int main() {
  // Select the graph type we wish to use
  typedef boost::adjacency_list < boost::vecS, boost::vecS, boost::undirectedS > UndirectedGraph;
  // Set up the vertex IDs and names
  enum { r, s, t, u, v, w, x, y, N };
  const char* name = "rstuvwxy";
  // Specify the edges in the graph
  typedef std::pair < int, int > E;
  E edge_array[] = { E(r, s), E(r, v), E(s, w), E(w, r), E(w, t),
    E(w, x), E(x, t), E(t, u), E(x, y), E(u, y)
  };

  // Number of edges in the graph. We need this to populate the graph using loop. sizeof(edge_array) = 80 and sizeof(E) = 8
  const int n_edges = sizeof(edge_array) / sizeof(E);

  // Populating the graph using for loop
  UndirectedGraph undigraph(N);
  for (std::size_t j = 0; j < n_edges; ++j)
    boost::add_edge(edge_array[j].first, edge_array[j].second, undigraph);

  // Typedefs
  typedef boost::graph_traits < UndirectedGraph >::vertices_size_type Size;
  
  // Imp Point: distance_map, predecessor_map, vertex_index_map, all type of maps is defined like " get(____, g) "

  // a vector to hold the discover time property for each vertex. Not a clear code the following 4 lines
  // iterator_property_map is a default of color_map, so basically we are making a color map here.
  std::vector < Size > discover_time(num_vertices(undigraph));
  typedef boost::iterator_property_map< std::vector<Size>::iterator,
          boost::property_map<UndirectedGraph, boost::vertex_index_t>::const_type> discovertime_propertymap_type;
  discovertime_propertymap_type discovertime_propertymap(discover_time.begin(), get(boost::vertex_index, undigraph));

  Size time = 0;

  // Creating a visitor obj
  bfs_time_visitor < discovertime_propertymap_type > vis(discovertime_propertymap, time);
  // Calling the bfs function
  boost::breadth_first_search(undigraph, vertex(s, undigraph), visitor(vis));

  // Use std::sort to order the vertices by their discover time
  std::vector<boost::graph_traits<UndirectedGraph>::vertices_size_type > discover_order(N);
  boost::integer_range < int >range(0, N);
  std::copy(range.begin(), range.end(), discover_order.begin());
  std::sort(discover_order.begin(), discover_order.end(),
            boost::indirect_cmp < discovertime_propertymap_type, std::less < Size > >(discovertime_propertymap));

  std::cout << "order of discovery: ";
  for (int i = 0; i < N; ++i)
    std::cout << name[discover_order[i]] << " ";
  std::cout << std::endl;

  return EXIT_SUCCESS;
}