How to traverse graph in boost use BFS

You can see here a list of the overloads of breadth_first_search. If you don't want to specify every one of the parameters you need to use the named-parameter version. It would look like this:

breadth_first_search(graph, a, boost::visitor(bfs_visitor));

This would work as is if you had used vecS as your VertexList storage in your graph definition or if you had constructed and initialized an internal vertex_index property map. Since you are using hash_setS you need to change the invocation to:

breath_first_search(graph, a, boost::visitor(bfs_visitor).vertex_index_map(my_index_map));

You are already using an index map in your uint32_t bundled property. You can use get(boost::vertex_bundle, graph) to access it.

There was also a problem with your visitor. You should derive it from boost::default_bfs_visitor and the graph_t parameter of your member functions needs to be const qualified.

Full code:

#include <stdint.h>
#include <iostream>
#include <vector>
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/breadth_first_search.hpp>

typedef boost::adjacency_list<boost::vecS, boost::hash_setS, boost::undirectedS, uint32_t, uint32_t, boost::no_property> graph_t;


struct my_visitor : boost::default_bfs_visitor{

    void initialize_vertex(const graph_t::vertex_descriptor &s, const graph_t &g) const {
      std::cout << "Initialize: " << g[s] << std::endl;
    }
    void discover_vertex(const graph_t::vertex_descriptor &s, const graph_t &g) const {
      std::cout << "Discover: " << g[s] << std::endl;
    }
    void examine_vertex(const graph_t::vertex_descriptor &s, const graph_t &g) const {
      std::cout << "Examine vertex: " << g[s] << std::endl;
    }
    void examine_edge(const graph_t::edge_descriptor &e, const graph_t &g) const {
      std::cout << "Examine edge: " << g[e] << std::endl;
    }
    void tree_edge(const graph_t::edge_descriptor &e, const graph_t &g) const {
      std::cout << "Tree edge: " << g[e] << std::endl;
    }
    void non_tree_edge(const graph_t::edge_descriptor &e, const graph_t &g) const {
      std::cout << "Non-Tree edge: " << g[e] << std::endl;
    }
    void gray_target(const graph_t::edge_descriptor &e, const graph_t &g) const {
      std::cout << "Gray target: " << g[e] << std::endl;
    }
    void black_target(const graph_t::edge_descriptor &e, const graph_t &g) const {
      std::cout << "Black target: " << g[e] << std::endl;
    }
    void finish_vertex(const graph_t::vertex_descriptor &s, const graph_t &g) const {
      std::cout << "Finish vertex: " << g[s] << std::endl;
    }
  };

int main() {
  graph_t graph(4);
  graph_t::vertex_descriptor a = boost::vertex(0, graph);
  graph_t::vertex_descriptor b = boost::vertex(1, graph);
  graph_t::vertex_descriptor c = boost::vertex(2, graph);
  graph_t::vertex_descriptor d = boost::vertex(3, graph);
  graph[a] = 0;
  graph[b] = 1;
  graph[c] = 2;
  graph[d] = 3;
  std::pair<graph_t::edge_descriptor, bool> result = boost::add_edge(a, b, 0, graph);
  result = boost::add_edge(a, c, 1, graph);
  result = boost::add_edge(c, b, 2, graph);

  my_visitor vis;

  breadth_first_search(graph, a, boost::visitor(vis).vertex_index_map(get(boost::vertex_bundle,graph)));
  return 0;
} 

I faced the same problem, but compared to the answer provided by user1252091 my vertex type is a struct that doesn't include an integer that can be used to create a vertex_index_map, therefore the line

breadth_first_search(graph, a, boost::visitor(vis).vertex_index_map(get(boost::vertex_bundle,graph)));

wouldn't work in my case. Eventually I figured out how to create an external vertex_index_map (thanks also to this answer) and pass it to the breadth_first_search function. Here is a working example in case it helps others:

#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/visitors.hpp>
#include <boost/graph/breadth_first_search.hpp>
#include <iostream>

struct Person
{
    std::string Name;
    unsigned int YearBorn;
};

typedef boost::adjacency_list <boost::vecS, boost::hash_setS, boost::bidirectionalS, Person, boost::no_property > FamilyTree;
typedef boost::graph_traits<FamilyTree>::vertex_descriptor  Vertex;
typedef boost::graph_traits<FamilyTree>::edge_descriptor    Edge;

template <class Graph>
class BfsVisitor : public boost::default_bfs_visitor
{
public:
    typedef typename boost::graph_traits<Graph>::vertex_descriptor VertexDescriptor;
    typedef typename boost::graph_traits<Graph>::edge_descriptor   EdgeDescriptor;

    BfsVisitor(std::vector<VertexDescriptor>& nodesVisited)
    : m_nodesVisited(nodesVisited){}

    void tree_edge(EdgeDescriptor e, const Graph& g) const
    {
        VertexDescriptor u = source(e, g);
        VertexDescriptor v = target(e, g);
        m_nodesVisited.push_back(v);
    }

private:
    std::vector<VertexDescriptor>& m_nodesVisited;
};


const Person Abe_Simpson        {"Abe_Simpson", 0};
const Person Mona_Simpson       { "Mona_Simpson", 0};
const Person Herb_Simpson       { "Herb_Simpson", 0};
const Person Homer_Simpson      { "Homer_Simpson", 0};

const Person Clancy_Bouvier     { "Clancy_Bouvier", 0};
const Person Jacqueline_Bouvier { "Jacqueline_Bouvier", 0};
const Person Marge_Bouvier      { "Marge_Bouvier", 0};
const Person Patty_Bouvier      { "Patty_Bouvier", 0};
const Person Selma_Bouvier      { "Selma_Bouvier", 0};

const Person Bart_Simpson       { "Bart_Simpson", 0};
const Person Lisa_Simpson       { "Lisa_Simpson", 0};
const Person Maggie_Simpson     { "Maggie_Simpson", 0};
const Person Ling_Bouvier       { "Ling_Bouvier", 0};





int main(void)
{
    std::cout << __FUNCTION__ << "\n";

    FamilyTree g;


    // nodes
    auto v_Abe_Simpson = boost::add_vertex(Abe_Simpson,g);
    auto v_Mona_Simpson = boost::add_vertex(Mona_Simpson,g);
    auto v_Herb_Simpson = boost::add_vertex(Herb_Simpson,g);
    auto v_Homer_Simpson = boost::add_vertex(Homer_Simpson,g);

    auto v_Clancy_Bouvier = boost::add_vertex(Clancy_Bouvier,g);
    auto v_Jacqueline_Bouvier = boost::add_vertex(Jacqueline_Bouvier,g);
    auto v_Marge_Bouvier = boost::add_vertex(Marge_Bouvier,g);
    auto v_Patty_Bouvier = boost::add_vertex(Patty_Bouvier,g);
    auto v_Selma_Bouvier = boost::add_vertex(Selma_Bouvier,g);

    auto v_Bart_Simpson = boost::add_vertex(Bart_Simpson,g);
    auto v_Lisa_Simpson = boost::add_vertex(Lisa_Simpson,g);
    auto v_Maggie_Simpson = boost::add_vertex(Maggie_Simpson,g);
    auto v_Ling_Bouvier = boost::add_vertex(Ling_Bouvier,g);

    // connections
    boost::add_edge(v_Abe_Simpson, v_Herb_Simpson, g);
    boost::add_edge(v_Abe_Simpson, v_Homer_Simpson, g);
    boost::add_edge(v_Mona_Simpson, v_Herb_Simpson, g);
    boost::add_edge(v_Mona_Simpson, v_Homer_Simpson, g);

    boost::add_edge(v_Clancy_Bouvier, v_Marge_Bouvier, g);
    boost::add_edge(v_Clancy_Bouvier, v_Patty_Bouvier, g);
    boost::add_edge(v_Clancy_Bouvier, v_Selma_Bouvier, g);
    boost::add_edge(v_Jacqueline_Bouvier, v_Marge_Bouvier, g);
    boost::add_edge(v_Jacqueline_Bouvier, v_Patty_Bouvier, g);
    boost::add_edge(v_Jacqueline_Bouvier, v_Selma_Bouvier, g);

    boost::add_edge(v_Homer_Simpson, v_Bart_Simpson, g);
    boost::add_edge(v_Homer_Simpson, v_Lisa_Simpson, g);
    boost::add_edge(v_Homer_Simpson, v_Maggie_Simpson, g);
    boost::add_edge(v_Marge_Bouvier, v_Bart_Simpson, g);
    boost::add_edge(v_Marge_Bouvier, v_Lisa_Simpson, g);
    boost::add_edge(v_Marge_Bouvier, v_Maggie_Simpson, g);

    boost::add_edge(v_Selma_Bouvier, v_Ling_Bouvier, g);


    typedef std::map<Vertex, size_t>IndexMap;
    IndexMap mapIndex;
    boost::associative_property_map<IndexMap> propmapIndex(mapIndex);
    size_t i=0;
    FamilyTree::vertex_iterator vi, vi_end;
    for (boost::tie(vi, vi_end) = boost::vertices(g); vi != vi_end; ++vi)
    {
        boost::put(propmapIndex, *vi, i++);
    }


    for (boost::tie(vi, vi_end) = boost::vertices(g); vi != vi_end; ++vi)
    {
        Vertex vParent = *vi;

        std::vector<Vertex> vertexDescriptors;
        BfsVisitor<FamilyTree> bfsVisitor(vertexDescriptors);
        breadth_first_search(g, vParent, visitor(bfsVisitor).vertex_index_map(propmapIndex));


        std::cout << "\nDecendants of " << g[vParent].Name << ":\n";
        for (auto v : vertexDescriptors)
        {   
            Person p = g[v];
            std::cout << p.Name << "\n";
        }   
    }

    getchar();
    return 0;
}