# 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:

• Works for undirected graphs.

• 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 edges'
);
node
------
3
6
7
8
(4 rows)



Nodes in red are the articulation points.

## 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 (node)

Column

Type

Description

node

BIGINT

Identifier of the vertex.