# pgr_kruskal¶

pgr_kruskal — Minimum spanning tree of a graph using Kruskal’s algorithm.

Availability

• Version 3.0.0

• New Official function

## Description¶

This algorithm finds the minimum spanning forest in a possibly disconnected graph using Kruskal’s algorithm.

The main Characteristics are:

• It’s implementation is only on undirected graph.

• Process is done only on edges with positive costs.

• When the graph is connected

• The resulting edges make up a tree

• When the graph is not connected,

• Finds a minimum spanning tree for each connected component.

• The resulting edges make up a forest.

• The total weight of all the edges in the tree or forest is minimized.

• Kruskal’s running time: $$O(E * log E)$$

• EMPTY SET is returned when there are no edges in the graph.

## Signatures¶

Summary

pgr_kruskal(Edges SQL)
RETURNS SET OF (edge, cost)
OR EMPTY SET
Example:

Minimum spanning forest

SELECT * FROM pgr_kruskal(
'SELECT id, source, target, cost, reverse_cost
FROM edges ORDER BY id'
) ORDER BY edge;
edge | cost
------+------
1 |    1
2 |    1
3 |    1
6 |    1
7 |    1
10 |    1
11 |    1
12 |    1
13 |    1
14 |    1
15 |    1
16 |    1
17 |    1
18 |    1
(14 rows)

## 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 (edge, cost)

Column

Type

Description

edge

BIGINT

Identifier of the edge.

cost

FLOAT

Cost to traverse the edge.