# pgr_biconnectedComponents¶

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

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

## 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.