# pgRouting Manual (3.1)

## pgr_articulationPoints

`pgr_articulationPoints` - Return the articulation points of an undirected graph.

Boost Graph Inside

Availability

- Version 3.0.0

  - Return columns change: `seq` is removed

  - Official function

- Version 2.5.0

  - New experimental function

Support

- Supported versions: current(3.1) 3.0

- Unsupported versions: 2.6 2.5

## 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)

- 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 `(node)`

Column | Type | Description
--- | --- | ---
node | `BIGINT` | Identifier of the vertex.

## See Also

- Components - Family of functions

- The queries use the Sample Data network.

- Boost: Biconnected components & articulation points

- wikipedia: Biconnected component

Indices and tables

- Index

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