# pgRouting Manual (3.1)

## pgr_biconnectedComponents

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

Boost Graph Inside

Availability

- Version 3.0.0

  - Return columns change:

    - `n_seq` is removed

    - `seq` changed type to `BIGINT`

  - Official function

- Version 2.5.0

  - New experimental function

Support

- Supported versions: current(3.1) 3.0

- Unsupported versions: 2.6 2.5

## 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:

- The signature is for an undirected graph.

- 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, edge)
    OR EMPTY SET

Example

  The biconnected components of the graph

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

## Parameters

Parameter | Type | Default | Description
--- | --- | --- | ---
Edges SQL | `TEXT` |  | Inner query as described below.

## Inner query

edges SQL

  an SQL query of an undirected graph, 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

## Result Columns

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

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

## See Also

- Components - Family of functions

- The queries use the Sample Data network.

- Boost: Biconnected components

- wikipedia: Biconnected component

Indices and tables

- Index

- Search Page