..
   ****************************************************************************
    pgRouting Manual
    Copyright(c) pgRouting Contributors

    This documentation is licensed under a Creative Commons Attribution-Share
    Alike 3.0 License: https://creativecommons.org/licenses/by-sa/3.0/
   ****************************************************************************


.. index::
   single: Components Family ; pgr_biconnectedComponents
   single: biconnectedComponents

|

``pgr_biconnectedComponents``
===============================================================================

``pgr_biconnectedComponents`` — Biconnected components of an undirected graph.

.. rubric:: Availability

* Version 3.0.0

  * Result columns change:

    * n_seq`` is removed
    * seq`` changed type to ``BIGINT``

  * Function promoted to official.

* Version 2.5.0

  * New experimental function.


Description
-------------------------------------------------------------------------------

The biconnected components of an undirected graph are the maximal subsets of
vertices such that the removal of a vertex from particular component will not
disconnect the component.
Unlike connected components, vertices may belong to multiple biconnected
components.
Vertices can be present in multiple biconnected components, but each edge can
only be contained in a single biconnected component.

**The main characteristics are:**

- Works for **undirected** graphs.
- Components are described by edges.
- The returned values are ordered:

  - ``component`` ascending.
  - ``edge`` ascending.

- Running time: :math:`O(V + E)`

|Boost| Boost Graph Inside

Signatures
-------------------------------------------------------------------------------

.. admonition:: \ \
   :class: signatures

   | pgr_biconnectedComponents(`Edges SQL`_)

   | Returns set of |result-component-E|
   | OR EMPTY SET

:Example: The biconnected components of the graph

.. literalinclude:: biconnectedComponents.queries
   :start-after: -- q1
   :end-before: -- q2

.. figure:: /images/bcc_sampledata.png
   :scale: 25%

Parameters
-------------------------------------------------------------------------------

.. include:: pgRouting-concepts.rst
   :start-after: only_edge_param_start
   :end-before: only_edge_param_end

Inner Queries
-------------------------------------------------------------------------------

Edges SQL
...............................................................................

.. include:: pgRouting-concepts.rst
    :start-after: basic_edges_sql_start
    :end-before: basic_edges_sql_end

Result columns
-------------------------------------------------------------------------------

Returns set of |result-component-E|

.. list-table::
   :width: 81
   :widths: auto
   :header-rows: 1

   * - Column
     - Type
     - Description
   * - ``seq``
     - ``BIGINT``
     - Sequential value starting from **1**.
   * - ``component``
     - ``BIGINT``
     - Component identifier.

       * Has the value of the minimum edge identifier in the component.
   * - ``edge``
     - ``BIGINT``
     - Identifier of the edge that belongs to the ``component``.

See Also
-------------------------------------------------------------------------------

* :doc:`components-family`
* :doc:`sampledata`
* `Boost: Biconnected components & articulation points
  <https://www.boost.org/libs/graph/doc/biconnected_components.html>`__
* wikipedia: `Biconnected component
  <https://en.wikipedia.org/wiki/Biconnected_component>`__

.. rubric:: Indices and tables

* :ref:`genindex`
* :ref:`search`
