如何使用 Boost 的 vf2_subgraph_iso 检测多图上的子图同构？

Question

我正在尝试使用 Boost 的 vf2_subgraph_iso() 来检测子图同构。

我可以在简单图上成功地做到这一点，但不能在multigraph（允许有多个边的图）上做到这一点。

考虑检测以下 G1 和 G2 之间的子图同构：

G1 是 G2 的子图，我想使用以下代码检测它：

#include <vector>
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/vf2_sub_graph_iso.hpp>

int main()
{
  // Define edge property
  typedef boost::property<
    boost::edge_name_t,
    char
  > edge_property;

  // Define graph type
  typedef boost::adjacency_list<
    boost::vecS,           // OutEdgeListS
    boost::vecS,           // VertexListS
    boost::bidirectionalS, // DirectedS
    boost::no_property,    // VertexProperties
    edge_property,         // EdgeProperties
    boost::no_property,    // GraphProperties
    boost::listS           // EdgeListS
  > MyGraphType;

  // Build graph G1
  MyGraphType g1;
  std::vector<MyGraphType::vertex_descriptor> v1(3);
  for (auto itr = v1.begin(); itr != v1.end(); ++itr) {
    *itr = boost::add_vertex(g1);
  }
  boost::add_edge(v1[0], v1[1], edge_property('a'), g1);
  boost::add_edge(v1[0], v1[2], edge_property('a'), g1);
  boost::add_edge(v1[1], v1[2], edge_property('b'), g1);

  // Build graph G2
  MyGraphType g2;
  std::vector<MyGraphType::vertex_descriptor> v2(3);
  for (auto itr = v2.begin(); itr != v2.end(); ++itr) {
    *itr = boost::add_vertex(g2);
  }
  boost::add_edge(v2[0], v2[1], edge_property('a'), g2);
  boost::add_edge(v2[0], v2[2], edge_property('a'), g2);
  boost::add_edge(v2[1], v2[2], edge_property('a'), g2);
  boost::add_edge(v2[1], v2[2], edge_property('b'), g2);

  // Create predicate of edge
  typedef boost::property_map<MyGraphType, boost::edge_name_t>::type edge_name_map_t;
  typedef boost::property_map_equivalent<edge_name_map_t, edge_name_map_t> edge_comp_t;
  edge_comp_t edge_comp = boost::make_property_map_equivalent(
    boost::get(boost::edge_name, g1), boost::get(boost::edge_name, g2));

  // Create callback
  boost::vf2_print_callback<MyGraphType, MyGraphType> callback(g1, g2);

  // Execute
  const bool result = boost::vf2_subgraph_iso(
    g1, g2, callback, boost::vertex_order_by_mult(g1),
    boost::edges_equivalent(edge_comp));

  std::cout << "subgraph isomorphic? " << std::boolalpha << result << std::endl;

  return 0;
}

预期结果：

(0, 0) (1, 1) (2, 2)
subgraph isomorphic? true

实际结果：

subgraph isomorphic? false

我的代码哪里错了？

对不起，我的英语很差。谢谢！

Answer 1

vf2_subgraph_iso 会比较边缘的属性。在您的代码中，边 1->2 的属性在 graph1 中是“b”，但在 graph2 中是“a”、“b”。所以它们不是同一个结构。

如果您希望它在仅匹配所有属性的一部分时返回 true，您可以按照您的规则使用结构和重载运算符“==”。 对于您的示例，以下代码就可以了。

#include <vector>
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/vf2_sub_graph_iso.hpp>

int main()
{
  // Define edge property
  struct  EdgeProperties {
      EdgeProperties() {}
      EdgeProperties(char elabel) { _elabels.emplace_back(elabel);}
      EdgeProperties(std::vector<char>& elabels) :_elabels(elabels) {}
      /* overload == */
      bool operator==(EdgeProperties const& other) const {
        for (auto& my_l:_elabels) {
          for (auto& o_l:other._elabels) {
            if (my_l == o_l) return true;
          }
        }
        return false;
      }
      std::vector<char> _elabels;
  };

  typedef boost::property<
    boost::edge_name_t,
    EdgeProperties
  > edge_property;

  // Define graph type
  typedef boost::adjacency_list<
    boost::vecS,           // OutEdgeListS
    boost::vecS,           // VertexListS
    boost::bidirectionalS, // DirectedS
    boost::no_property,    // VertexProperties
    edge_property,         // EdgeProperties
    boost::no_property,    // GraphProperties
    boost::listS           // EdgeListS
  > MyGraphType;

  // Build graph G1
  MyGraphType g1;
  std::vector<MyGraphType::vertex_descriptor> v1(3);
  for (auto itr = v1.begin(); itr != v1.end(); ++itr) {
    *itr = boost::add_vertex(g1);
  }
  boost::add_edge(v1[0], v1[1], edge_property('a'), g1);
  boost::add_edge(v1[0], v1[2], edge_property('a'), g1);
  boost::add_edge(v1[1], v1[2], edge_property('b'), g1);

  // Build graph G2
  MyGraphType g2;
  std::vector<MyGraphType::vertex_descriptor> v2(3);
  for (auto itr = v2.begin(); itr != v2.end(); ++itr) {
    *itr = boost::add_vertex(g2);
  }
  boost::add_edge(v2[0], v2[1], edge_property('a'), g2);
  boost::add_edge(v2[0], v2[2], edge_property('a'), g2);
  std::vector<char> tmp;
  tmp.emplace_back('a');
  tmp.emplace_back('b');
  boost::add_edge(v2[1], v2[2], edge_property(tmp), g2);

  // Create predicate of edge
  typedef boost::property_map<MyGraphType, boost::edge_name_t>::type edge_name_map_t;
  typedef boost::property_map_equivalent<edge_name_map_t, edge_name_map_t> edge_comp_t;
  edge_comp_t edge_comp = boost::make_property_map_equivalent(
    boost::get(boost::edge_name, g1), boost::get(boost::edge_name, g2));

  // Create callback
  boost::vf2_print_callback<MyGraphType, MyGraphType> callback(g1, g2);

  // Execute
  const bool result = boost::vf2_subgraph_iso(
    g1, g2, callback, boost::vertex_order_by_mult(g1),
    boost::edges_equivalent(edge_comp));

  std::cout << "subgraph isomorphic? " << std::boolalpha << result << std::endl;

  return 0;
}