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Bug in biconnected_components when handling multiple (parallel) edges between the same pair of vertices

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#434 2 comments 0 reactions 1 assignee View on GitHub

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@jeremy-murphy is already working on this.

Since Oct 7, 2025.

  • #435 by @GlebGrishuhin — open

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Description

algorithm priority: high
Version of Boost

1.88.0

Problem description

In a block of parallel edges (e.g., three edges between A and B), only one edge receives the correct biconnected component label.
The rest are incorrectly assigned component ID 0 — even though they belong to the same biconnected component.

Expected behavior

All edges in a block of parallel edges should have the same non-zero component ID

Actual behavior

Only one edge gets the correct component ID; others are assigned 0 — which is wrong

Reproducible example

Problem can be reproduced with such program.

#include <boost/config.hpp>
#include <vector>
#include <list>
#include <boost/graph/biconnected_components.hpp>
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/properties.hpp>
#include <boost/property_map/property_map.hpp>
#include <iterator>
#include <iostream>

namespace boost
{
    struct edge_component_t
    {
        typedef edge_property_tag kind;
    } edge_component;
}

int main()
{
    using namespace boost;
    typedef adjacency_list<vecS, vecS, undirectedS,
        property<boost::vertex_index_t, std::size_t>,
        property<edge_component_t, std::size_t>  
    > graph_t;

    typedef graph_traits<graph_t>::vertex_descriptor vertex_t;
    typedef graph_traits<graph_t>::vertices_size_type size_type;

    std::vector<std::pair<size_t, size_t>> graph_edges = {
        {0, 1}, {0, 1}, {0, 1}, // block of parallel edges
        {1, 2}, // bridge
        {2, 3}, {2, 3}, {2, 3}, // block of parallel edges
        {3, 4}, // bridge
        {4, 5} // bridge
    };

    graph_t g(graph_edges.size());

    for (const auto& pair : graph_edges)
        add_edge(pair.first, pair.second, g);

    property_map<graph_t, edge_component_t>::type comp_map = get(edge_component, g);

    std::vector<vertex_t> art_points; 

    auto num_comps = biconnected_components(g, comp_map, std::back_inserter(art_points));

    std::cerr << "Found " << num_comps.first << " biconnected components.\n";
    std::cerr << "Found " << art_points.size() << " articulation points.\n";

    graph_traits<graph_t>::edge_iterator ei, ei_end;
    for (boost::tie(ei, ei_end) = edges(g); ei != ei_end; ++ei)
        std::cout << (char)(source(*ei, g) + 'A') << " -- "
        << (char)(target(*ei, g) + 'A')
        << " " << comp_map[*ei] << "\n";

    return 0;
}
Actual output

The proram output contains block index for each edge of graph:

Found 5 biconnected components.
Found 4 articulation points.
A -- B 4
A -- B 0
A -- B 0
B -- C 3
C -- D 2
C -- D 0
C -- D 0
D -- E 1
E -- F 0

Only one of parallel edges A-B has non-zero block index. Same stands for edges C-D.

Picture shows the graph from example. Red vertices indicate articulation points. Each edge is labeled with index of biconnected component (block) to which it belongs Picture makes clear that output of example is incorrect - each group of parallel edges should form a distinct block.

Image
Expected output
Found 5 biconnected components.
Found 4 articulation points.
A -- B 4
A -- B 4
A -- B 4
B -- C 3
C -- D 2
C -- D 2
C -- D 2
D -- E 1
E -- F 0
Dominant language
C++
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Merged PRs (30d)
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