pgr_articulationPoints

pgr_articulationPoints - Return the articulation points of an undirected graph.

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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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