# pgr_transitiveClosure - Experimental¶

pgr_transitiveClosure — Transitive closure graph of a directed graph.

Warning

Possible server crash

• These functions might create a server crash

Warning

Experimental functions

• They are not officially of the current release.

• They likely will not be officially be part of the next release:

• The functions might not make use of ANY-INTEGER and ANY-NUMERICAL

• Name might change.

• Signature might change.

• Functionality might change.

• pgTap tests might be missing.

• Might need c/c++ coding.

• May lack documentation.

• Documentation if any might need to be rewritten.

• Documentation examples might need to be automatically generated.

• Might need a lot of feedback from the comunity.

• Might depend on a proposed function of pgRouting

• Might depend on a deprecated function of pgRouting

Availability

• Version 3.0.0

• New experimental function

## Description¶

Transforms the input directed graph into the transitive closure of the graph.

The main characteristics are:

• Process is valid for directed graphs.

• The transitive closure of an undirected graph produces a cluster graph

• Reachability between vertices on an undirected graph happens when they belong to the same connected component. (see pgr_connectedComponents)

• The returned values are not ordered

• The returned graph is compresed

• Running time: $$O(|V||E|)$$

## Signatures¶

Summary

The pgr_transitiveClosure function has the following signature:

pgr_transitiveClosure(Edges SQL)
RETURNS SET OF (seq, vid, target_array)
Example:

Rechability of a subgraph

SELECT * FROM pgr_transitiveclosure(
'SELECT id, source, target, cost, reverse_cost
FROM edges WHERE id IN (2, 3, 5, 11, 12, 13, 15)')
ORDER BY vid;
seq | vid |    target_array
-----+-----+--------------------
1 |   6 | {}
6 |   8 | {12,17,16}
2 |  10 | {12,17,16,11,6}
4 |  11 | {12,17,16}
5 |  12 | {17,16}
3 |  15 | {12,17,16,10,11,6}
8 |  16 | {17,16}
7 |  17 | {17,16}
(8 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 (seq, vid, target_array)

Column

Type

Description

seq

INTEGER

Sequential value starting from $$1$$

vid

BIGINT

Identifier of the source of the edges

target_array

BIGINT

Identifiers of the targets of the edges

• Identifiers of the vertices that are reachable from vertex v.