# pgRouting Manual (3.6)

## pgr_articulationPoints

# `pgr_articulationPoints`

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

Boost Graph Inside

Availability

- Version 3.0.0

  - Result 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.

## 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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