# pgr_articulationPoints¶

pgr_articulationPoints - Return the articulation points of an undirected graph.

Availability

• Version 3.0.0

• Return columns change: seq is removed

• Official function

• Version 2.5.0

• New experimental function

## Description¶

Those vertices that belong to more than one biconnected component are called articulation points or, equivalently, cut vertices. Articulation points are vertices whose removal would increase the number of connected components in the graph. This implementation can only be used with an undirected graph.

The main characteristics are:

• The signature is for an undirected graph.

• The returned values are ordered:

• node ascending

• Running time: $$O(V + E)$$

## Signatures¶

pgr_articulationPoints(Edges SQL)

RETURNS SET OF (node)
OR EMPTY SET

Example

The articulation points of the graph

SELECT * FROM pgr_articulationPoints(
'SELECT id, source, target, cost, reverse_cost FROM edge_table'
);
node
------
2
5
8
10
(4 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)

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 (node)

Column

Type

Description

node

BIGINT

Identifier of the vertex.