这是几乎使用 connected_components。

复杂的事情是忽略PH节点。您没有说该节点是给出的还是应检测到。我写了一些代码来检测它。

让我们开始

#include <boost/graph/adjacency_list.hpp>
using Graph = boost::adjacency_list<boost::vecS, boost::vecS, boost::bidirectionalS,
    boost::property<boost::vertex_name_t, std::string> >;

我们要大致实现以下步骤：

using ComponentId = int;
using Mappings    = std::vector<ComponentId>;
using Graphs      = std::vector<Graph>;
Graph build();
Mappings map_components(Graph const&);
Graphs split(Graph const&, Mappings const&);

，主程序看起来像

#include <boost/graph/graph_utility.hpp>
int main() {
    Graph g = build();
    Mappings components = map_components(g);
    for (auto& sub : split(g, components)) {
        std::cout << "n========================n";
        print_graph(sub, get(boost::vertex_name, sub));
    }
}

样本数据

这很简单，因为我们使用了vertex_name属性：

using Vertex = Graph::vertex_descriptor;
Graph build() {
    Graph g;
    Vertex PH = add_vertex({"PH"}, g);
    Vertex PH1 = add_vertex({"PH1"}, g);
    Vertex PH2 = add_vertex({"PH2"}, g);
    Vertex N1 = add_vertex({"N1"}, g);
    Vertex N2 = add_vertex({"N2"}, g);
    Vertex N3 = add_vertex({"N3"}, g);
    Vertex N4 = add_vertex({"N4"}, g);
    add_edge(PH, PH1, g);
    add_edge(PH, PH2, g);
    add_edge(PH1, N1, g);
    add_edge(PH1, N2, g);
    add_edge(PH2, N3, g);
    add_edge(PH2, N4, g);
    return g;
}

映射组件

这还不错：

#include <boost/graph/connected_components.hpp> // connected_components
Mappings naive_components(Graph const& g) {
    Mappings mappings(num_vertices(g));
    int num = boost::connected_components(g, mappings.data());
    return mappings;
}

除了连接所有内容，所以我们得到1个包含所有顶点的组件...让我们使用articulation_points首先"忽略"顶点：

#include <boost/graph/biconnected_components.hpp> // articulation_points
#include <boost/graph/connected_components.hpp> // connected_components
#include <boost/graph/filtered_graph.hpp>
#include <boost/function.hpp>
using Filtered = boost::filtered_graph<Graph, boost::keep_all, boost::function<bool(Vertex)> >;
Mappings map_components(Graph const& g) {
    Mappings mappings(num_vertices(g));
    std::vector<Vertex> ap;
    articulation_points(g, back_inserter(ap));
    if (!ap.empty()) {
        // get the articulation point with the lowest degree
        nth_element(ap.begin(), ap.begin()+1, ap.end(), [&](Vertex a, Vertex b) { return degree(a, g) < degree(b, g); });
        Vertex ignored = ap.front();
        std::cout << "Igoring articulation point " << get(boost::vertex_name, g, ignored) << " from graphn";
        Filtered fg(g, {}, [&](Vertex v) { return ignored != v; });
        int num = boost::connected_components(fg, mappings.data());
        mappings[ignored] = num; // make sure the ignored vertex is in its own component
    }
    return mappings;
}

基本上是在做同样的事情，但它忽略了PH节点。请注意，我们尝试确保剪切尽可能少的边缘（通过degree进行排序）。

拆分

将单独的图分解成几乎是一种形式（重复使用相同的Filtered图表）：

#include <boost/graph/copy.hpp>
Graphs split(Graph const& g, Mappings const& components) {
    if (components.empty())
        return {};
    Graphs results;
    auto highest = *std::max_element(components.begin(), components.end());
    for (int c = 0; c <= highest; ++c) {
        results.emplace_back();
        boost::copy_graph(Filtered(g, {}, [c, &components](Vertex v) { return components.at(v) == c; }), results.back());
    }
    return results;
}

完整列表

活在coliru

#include <boost/graph/adjacency_list.hpp>
using Graph = boost::adjacency_list<boost::vecS, boost::vecS, boost::bidirectionalS, boost::property<boost::vertex_name_t, std::string> >;
using ComponentId = int;
using Mappings    = std::vector<ComponentId>;
using Graphs      = std::vector<Graph>;
Graph build();
Mappings map_components(Graph const&);
Graphs split(Graph const&, Mappings const&);
#include <boost/graph/graph_utility.hpp>
int main() {
    Graph g = build();
    Mappings components = map_components(g);
    for (auto& sub : split(g, components)) {
        std::cout << "n========================n";
        print_graph(sub, get(boost::vertex_name, sub));
    }
}
using Vertex = Graph::vertex_descriptor;
Graph build() {
    Graph g;
    Vertex PH = add_vertex({"PH"}, g);
    Vertex PH1 = add_vertex({"PH1"}, g);
    Vertex PH2 = add_vertex({"PH2"}, g);
    Vertex N1 = add_vertex({"N1"}, g);
    Vertex N2 = add_vertex({"N2"}, g);
    Vertex N3 = add_vertex({"N3"}, g);
    Vertex N4 = add_vertex({"N4"}, g);
    add_edge(PH, PH1, g);
    add_edge(PH, PH2, g);
    add_edge(PH1, N1, g);
    add_edge(PH1, N2, g);
    add_edge(PH2, N3, g);
    add_edge(PH2, N4, g);
    return g;
}
#include <boost/graph/biconnected_components.hpp> // articulation_points
#include <boost/graph/connected_components.hpp> // connected_components
#include <boost/graph/filtered_graph.hpp>
#include <boost/function.hpp>
using Filtered = boost::filtered_graph<Graph, boost::keep_all, boost::function<bool(Vertex)> >;
Mappings map_components(Graph const& g) {
    Mappings mappings(num_vertices(g));
    std::vector<Vertex> ap;
    articulation_points(g, back_inserter(ap));
    if (!ap.empty()) {
        // get the articulation point with the lowest degree
        nth_element(ap.begin(), ap.begin()+1, ap.end(), [&](Vertex a, Vertex b) { return degree(a, g) < degree(b, g); });
        Vertex ignored = ap.front();
        std::cout << "Igoring articulation point " << get(boost::vertex_name, g, ignored) << " from graphn";
        Filtered fg(g, {}, [&](Vertex v) { return ignored != v; });
        int num = boost::connected_components(fg, mappings.data());
        mappings[ignored] = num; // make sure the ignored vertex is in its own component
    }
    return mappings;
}
#include <boost/graph/copy.hpp>
Graphs split(Graph const& g, Mappings const& components) {
    if (components.empty())
        return {};
    Graphs results;
    auto highest = *std::max_element(components.begin(), components.end());
    for (int c = 0; c <= highest; ++c) {
        results.emplace_back();
        boost::copy_graph(Filtered(g, {}, [c, &components](Vertex v) { return components.at(v) == c; }), results.back());
    }
    return results;
}

打印

Igoring articulation point PH from graph
========================
PH1 --> N1 N2 
N1 --> 
N2 --> 
========================
PH2 --> N3 N4 
N3 --> 
N4 --> 
========================
PH -->