# pgRouting Manual (2.5)

## pgr_biconnectedComponents - Experimental

`pgr_biconnectedComponents` — Return the biconnected components of an undirected graph. In particular, the algorithm implemented by Boost.Graph.

Boost Graph Inside

Warning

Experimental functions

- They are not officially of the current release.
- They likely will not be officially be part of the next release:
  - The functions might not make use of ANY-INTEGER and ANY-NUMERICAL
  - Name might change.
  - Signature might change.
  - Functionality might change.
  - pgTap tests might be missing.
  - Might need c/c++ coding.
  - May lack documentation.
  - Documentation if any might need to be rewritten.
  - Documentation examples might need to be automatically generated.
  - Might need a lot of feedback from the comunity.
  - Might depend on a proposed function of pgRouting
  - Might depend on a deprecated function of pgRouting

## Synopsis

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. So, the output only has edge version.

This implementation can only be used with an undirected graph.

## Characteristics

The main Characteristics are:

> - Components are described by edges
> - The returned values are ordered:
>   - component ascending
>   - edge ascending
> - Running time: \(O(V + E)\)

## Signatures

    pgr_biconnectedComponents(edges_sql)

    RETURNS SET OF (seq, component, n_seq, edge)
        OR EMPTY SET

The signature is for a undirected graph.

Example: |

    SELECT * FROM pgr_biconnectedComponents(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table'
    );
     seq | component | n_seq | edge
    -----+-----------+-------+------
       1 |         1 |     1 |    1
       2 |         2 |     1 |    2
       3 |         2 |     2 |    3
       4 |         2 |     3 |    4
       5 |         2 |     4 |    5
       6 |         2 |     5 |    8
       7 |         2 |     6 |    9
       8 |         2 |     7 |   10
       9 |         2 |     8 |   11
      10 |         2 |     9 |   12
      11 |         2 |    10 |   13
      12 |         2 |    11 |   15
      13 |         2 |    12 |   16
      14 |         6 |     1 |    6
      15 |         7 |     1 |    7
      16 |        14 |     1 |   14
      17 |        17 |     1 |   17
      18 |        18 |     1 |   18
    (18 rows)

## Description of the Signatures

### Description of the edges_sql query for components functions

edges_sql: | an SQL query, which should return a set of rows with the following columns:

Column | Type | Default | Description
--- | --- | --- | ---
id | `ANY-INTEGER` |  | Identifier of the edge.
source | `ANY-INTEGER` |  | Identifier of the first end point vertex of the edge.
target | `ANY-INTEGER` |  | Identifier of the second end point vertex of the edge.

cost

`ANY-NUMERICAL`

Weight of the edge (source, target)

- When negative: edge (source, target) does not exist, therefore it’s not part of the graph.

reverse_cost

`ANY-NUMERICAL`

-1

Weight of the edge (target, source),

- When negative: edge (target, source) does not exist, therefore it’s not part of the graph.

Where:

ANY-INTEGER: | SMALLINT, INTEGER, BIGINT
ANY-NUMERICAL: | SMALLINT, INTEGER, BIGINT, REAL, FLOAT

### Description of the parameters of the signatures

Parameter | Type | Default | Description
--- | --- | --- | ---
edges_sql | `TEXT` |  | SQL query as described above.

### Description of the return values for biconnected components, connected components (edge version) and strongly connected components

Returns set of `(seq, component, n_seq, edge)`

Column | Type | Description
--- | --- | ---
seq | `INT` | Sequential value starting from 1.
component | `BIGINT` | Component identifier. It is equal to the minimum edge identifier in the component.
n_seq | `INT` | It is a sequential value starting from 1 in a component.
edge | `BIGINT` | Identifier of the edge.

## See Also

- http://en.wikipedia.org/wiki/Biconnected_component
- The queries use the Sample Data network.

Indices and tables

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