# pgRouting Manual (3.6)

## pgr_transitiveClosure - Experimental

# `pgr_transitiveClosure` - Experimental

`pgr_transitiveClosure` — Transitive closure graph of a directed graph.

Boost Graph Inside

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.

## See Also

- Sample Data

- https://en.wikipedia.org/wiki/Transitive_closure

Indices and tables

- Index

- Search Page