pgr_biconnectedComponents

pgr_biconnectedComponents — Biconnected components of an undirected 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

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: \(O(V + E)\)

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 edges'
);
 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	Description
Edges SQL	TEXT	Edges SQL as described below.

Inner Queries

Edges SQL

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)
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. Has the value of the minimum edge identifier in the component.
edge	BIGINT	Identifier of the edge that belongs to the component.

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