1.方法一使用kruskal算法求最小生成树

思路
（1）新建一个存放边的容器std::vector < Edge > spanning_tree;
（2）调用 kruskal_minimum_spanning_tree将边放入容器中

#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/kruskal_min_spanning_tree.hpp>
#include <iostream>

int main()
{
  using namespace boost;
  typedef adjacency_list < vecS, vecS, undirectedS,no_property, property < edge_weight_t, int > > Graph;
  typedef graph_traits < Graph >::edge_descriptor Edge;
  typedef std::pair<int, int> E;

  const int num_nodes = 5;
  E edge_array[] = { E(0, 2), E(1, 3), E(1, 4), E(2, 1), E(2, 3),
    E(3, 4), E(4, 0), E(4, 1)
  };
  int weights[] = { 1, 1, 2, 7, 3, 1, 1, 1 };
  std::size_t num_edges = sizeof(edge_array) / sizeof(E);

  Graph g(edge_array, edge_array + num_edges, weights, num_nodes);

  property_map < Graph, edge_weight_t >::type weight = get(edge_weight, g);
  std::vector < Edge > spanning_tree;

  kruskal_minimum_spanning_tree(g, std::back_inserter(spanning_tree));
  std::cout << "Print the edges in the MST:" << std::endl;
  for (std::vector < Edge >::iterator ei = spanning_tree.begin();
       ei != spanning_tree.end(); ++ei) {
    std::cout << source(*ei, g) << " <--> " << target(*ei, g)
      << " with weight of " << weight[*ei]
      << std::endl;
  }
  return EXIT_SUCCESS;
}

参考文献
http://www.boost.org/doc/libs/1_64_0/libs/graph/example/kruskal-example.cpp