How to Create a C++ Boost Undirected Graph and Traverse It in Depth First Search (Dfs) Order

How to create a C++ Boost undirected graph and traverse it in depth first search (DFS) order?

// Boost DFS example on an undirected graph.
// Create a sample graph, traverse its nodes
// in DFS order and print out their values.

#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/depth_first_search.hpp>
#include <iostream>
using namespace std;

typedef boost::adjacency_list<boost::listS, boost::vecS, boost::undirectedS> MyGraph;
typedef boost::graph_traits<MyGraph>::vertex_descriptor MyVertex;

class MyVisitor : public boost::default_dfs_visitor
{
public:
  void discover_vertex(MyVertex v, const MyGraph& g) const
  {
    cerr << v << endl;
    return;
  }
};

int main()
{
  MyGraph g;
  boost::add_edge(0, 1, g);
  boost::add_edge(0, 2, g);
  boost::add_edge(1, 2, g);
  boost::add_edge(1, 3, g);

  MyVisitor vis;
  boost::depth_first_search(g, boost::visitor(vis));

  return 0;
}

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;
} 

boost minimum spanning tree, how to do depth first?

Update:
sehe gives an updated and more efficient solution here:
https://stackoverflow.com/a/49429372/85371

Here is a solution to the problem and good example of Kruskal and writing a custom DFS visitors. It should run as is. Example output in shown in the code below as to be self contained. As I mentioned in the comment the output of the MST algorithm is a set of edges. This shows you how to construct a new graph using that data.

Example take from http://en.wikipedia.org/wiki/Kruskals_algorithm.

Any suggestions for improvement would be appreciated. Thanks.

/**

Kruskal example from http://en.wikipedia.org/wiki/Kruskal's_algorithm

MST followed by DFS

Written by Paul W. Bible

*/
#include <iostream>
#include <vector>

#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/depth_first_search.hpp>
#include <boost/graph/kruskal_min_spanning_tree.hpp>

using namespace std;
using namespace boost;

typedef adjacency_list < vecS, vecS, undirectedS,
                    property< vertex_index_t, size_t> ,
                    property< edge_index_t, size_t, property<edge_weight_t,double> > > Graph;

typedef graph_traits<Graph>::vertex_descriptor Vertex;
typedef graph_traits<Graph>::edge_descriptor Edge;

typedef boost::property_map< Graph, boost::vertex_index_t>::type VertexIndexMap;
typedef boost::property_map< Graph, boost::edge_weight_t>::type WeightMap;

//DFS visitor, got help from http://stackoverflow.com/questions/14126/how-to-create-a-c-boost-undirected-graph-and-traverse-it-in-depth-first-search
// and http://www.boost.org/doc/libs/1_55_0/libs/graph/example/dfs-example.cpp
struct MyVis:default_dfs_visitor{
    //Default dfs is templeted to work with any Edge or Graph class
    // you will need to pass external graph info to the class
    MyVis(vector<string> vNames):vertNames(vNames){}

    template < typename Edge, typename Graph >
    void tree_edge(Edge e, const Graph& g) const {
        //This works since all graph verts will have an index
        VertexIndexMap vMap = get(boost::vertex_index,g);
        //print output message, source and target get the edge vertices
        cout << "Edge " << vertNames.at(vMap[source(e,g)]) <<  " " << vertNames.at(vMap[target(e,g)]) << endl;
        //cout << vertNames.size() << endl;
    }

private:
    vector<string> vertNames;
};

int main(int argc, char* argv[]){

    Graph G;

    vector<Vertex> verts;
    vector<Edge> edges;

    /* Vertices
    0   A
    1   B
    2   C
    3   D
    4   E
    5   F
    6   G
    */

    //add 7 vertices
    for(size_t i = 0; i < 7; ++i){
        Vertex v = add_vertex(G);
        verts.push_back(v);
    }

    //vertex to index map, typdef above
    VertexIndexMap vertexIndexMap = get(boost::vertex_index, G);

    vector<string> vertexNames(num_vertices(G));
    // Create the external property map, this map wraps the storage vector vertexNames
    boost::iterator_property_map< std::vector< string >::iterator, VertexIndexMap >
        vertexNameMap(vertexNames.begin(), vertexIndexMap);

    //set names
    vertexNames.at(0) = "A";
    vertexNames.at(1) = "B";
    vertexNames.at(2) = "C";
    vertexNames.at(3) = "D";
    vertexNames.at(4) = "E";
    vertexNames.at(5) = "F";
    vertexNames.at(6) = "G";

    //get internal weight map
    WeightMap weightMap = get(edge_weight,G);

    //Edge 1 A -> B, weight 7
    pair<Edge,bool> myPair = add_edge(verts.at(0),verts.at(1),G);
    edges.push_back(myPair.first);

    weightMap[myPair.first] = 7.0;
    //Edge 2 A -> D, weight 5
    myPair = add_edge(verts.at(0),verts.at(3),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 5.0;

    //Edge 3 B -> C, weight 8
    myPair = add_edge(verts.at(1),verts.at(2),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 8.0;
    //Edge 4 B -> D, weight 9
    myPair = add_edge(verts.at(1),verts.at(3),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 9.0;
    //Edge 5 B -> E, weight 7
    myPair = add_edge(verts.at(1),verts.at(4),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 7.0;

    //Edge 6 C -> E, weight 5
    myPair = add_edge(verts.at(2),verts.at(4),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 5.0;

    //Edge 7 D -> E, weight 15
    myPair = add_edge(verts.at(3),verts.at(4),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 15.0;
    //Edge 8 D -> F, weight 6
    myPair = add_edge(verts.at(3),verts.at(5),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 6.0;

    //Edge 9 E -> F, weight 8
    myPair = add_edge(verts.at(4),verts.at(5),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 8.0;
    //Edge 10 E -> G, weight 9
    myPair = add_edge(verts.at(4),verts.at(6),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 9.0;

    //Edge 11 F -> G, weight 11
    myPair = add_edge(verts.at(5),verts.at(6),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 11.0;

    //output
    cout << "vertices " << num_vertices(G) << endl;
    cout << "edges    " << num_edges(G) << endl;

    //create a stoage vector for MST edges
    vector<Edge> spanning_tree_edges;
    kruskal_minimum_spanning_tree(G, std::back_inserter(spanning_tree_edges));

    cout << "num MST edges " << spanning_tree_edges.size() << endl;

    //create a graph for the MST
    Graph MST;

    //get a weight map for the MST, may be used later
    WeightMap mstWeightMap = get(edge_weight,MST);

    //create a list of original names for the MST graph.
    vector<string> mstNames(num_vertices(G)); //the MST must span all verts in G
    //Index map for verts in MST, all graphs use an indepenent index system.
    VertexIndexMap mstIndexMap = get(boost::vertex_index, MST);

    cout << "MST Edges" << endl;
    for(size_t i = 0; i < spanning_tree_edges.size(); ++i){
        //get the edge
        Edge e = spanning_tree_edges.at(i);
        //get the vertices
        Vertex v1 = source(e,G);
        Vertex v2 = target(e,G);

        // output edge information
        cout << "edge weight " << weightMap[e] << " v1 " << vertexNameMap[v1] << " v2 " << vertexNameMap[v2] << endl;

        //insert the edge to the MST graph
        // Both graphs will share the vertices in verts list.
        myPair = add_edge(v1,v2,MST);

        //set the correct weights
        // may be needed at some point
        Edge mstE = myPair.first;
        mstWeightMap[mstE] = weightMap[e];

        //get the vertex index in the MST and set the name to that of original graph
        // mstNames will be used by the visitor
        mstNames.at(mstIndexMap[v1]) = vertexNameMap[v1];
        mstNames.at(mstIndexMap[v2]) = vertexNameMap[v2];

    }

    //Create your custom visitor and pass names to the visitor
    MyVis vis(mstNames);

    cout << "DFS on MST: start node E" << endl;
    //call dfs, see visitor implimentation above.
    boost::depth_first_search(MST, visitor(vis).root_vertex(verts.at(4)));

    cout << "DFS on MST: start node B" << endl;
    //call dfs, see visitor implimentation above.
    boost::depth_first_search(MST, visitor(vis).root_vertex(verts.at(1)));

    /* output
    vertices 7
    edges    11
    num MST edges 6
    MST Edges
    edge weight 5 v1 A v2 D
    edge weight 5 v1 C v2 E
    edge weight 6 v1 D v2 F
    edge weight 7 v1 B v2 E
    edge weight 7 v1 A v2 B
    edge weight 9 v1 E v2 G
    DFS on MST: start node E
    Edge E C
    Edge E B
    Edge B A
    Edge A D
    Edge D F
    Edge E G
    DFS on MST: start node B
    Edge B E
    Edge E C
    Edge E G
    Edge B A
    Edge A D
    Edge D F

    */

    //hold for output
    cin.get();
}

Cycles in an Undirected Graph

I think that depth first search solves it. If an unexplored edge leads to a node visited before, then the graph contains a cycle. This condition also makes it O(n), since you can explore maximum n edges without setting it to true or being left with no unexplored edges.

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