# pgRouting Manual (3.0-rc1)

## pgr_transitiveClosure - Experimental

`pgr_transitiveClosure` — Returns the transitive closure graph of the input graph. In particular, the transitive closure algorithm implemented by Boost.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

Support

- Supported versions: current(3.0)

## Description

The transitive_closure() function transforms the input graph g into the transitive closure graph tc.

This implementation can only be used with a directed graph with no cycles i.e. directed acyclic graph.

The main characteristics are:
  - Process is valid for directed acyclic graphs only. otherwise it will throw warnings.
  - The returned values are not ordered:
  - Running time: \(O(|V||E|)\)

## Signatures

Summary

The pgr_transitiveClosure function has the following signature:

    pgr_transitiveClosure(Edges SQL)
    RETURNS SETOF (id, vid, target_array)

Example: | Complete Graph of 3 vertexs

    SELECT * FROM pgr_transitiveclosure(
      'SELECT id,source,target,cost,reverse_cost FROM edge_table1'
    );
     seq | vid | target_array
    -----+-----+--------------
       1 |   0 | {1,3,2}
       2 |   1 | {3,2}
       3 |   3 | {2}
       4 |   2 | {}
    (4 rows)

## Parameters

Column | Type | Description
--- | --- | ---
Edges SQL | `TEXT` | SQL query as described in Inner query

## Inner query

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)

- When negative: edge (source, target) does not exist, therefore it’s not part of the graph.

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 SETOF (seq, vid, target_array)

The function returns a single row. The columns of the row are:

Column | Type | Description
--- | --- | ---
seq | `INTEGER` | Sequential value starting from 1.
vid | `BIGINT` | Identifier of the vertex.
target_array | `ARRAY[BIGINT]` | Array of identifiers of the vertices that are reachable from vertex v.

## Additional Examples

Example: | Some sub graphs of the sample data

    SELECT * FROM pgr_transitiveclosure(
      'SELECT id,source,target,cost,reverse_cost FROM edge_table where id=2'
    );
     seq | vid | target_array
    -----+-----+--------------
       1 |   2 | {}
       2 |   3 | {2}
    (2 rows)

    SELECT * FROM pgr_transitiveclosure(
      'SELECT id,source,target,cost,reverse_cost FROM edge_table where id=3'
    );
     seq | vid | target_array
    -----+-----+--------------
       1 |   3 | {}
       2 |   4 | {3}
    (2 rows)

    SELECT * FROM pgr_transitiveclosure(
      'SELECT id,source,target,cost,reverse_cost FROM edge_table where id=2 or id=3'
    );
     seq | vid | target_array
    -----+-----+--------------
       1 |   2 | {}
       2 |   3 | {2}
       3 |   4 | {3,2}
    (3 rows)

    SELECT * FROM pgr_transitiveclosure(
      'SELECT id,source,target,cost,reverse_cost FROM edge_table where id=11'
    );
     seq | vid | target_array
    -----+-----+--------------
       1 |   6 | {11}
       2 |  11 | {}
    (2 rows)

    -- q3
    SELECT * FROM pgr_transitiveclosure(
      'SELECT id,source,target,cost,reverse_cost FROM edge_table where cost=-1 or reverse_cost=-1'
    );
     seq | vid | target_array
    -----+-----+---------------
       1 |   2 | {}
       2 |   3 | {11,12,6,2}
       3 |   4 | {11,12,3,6,2}
       4 |   6 | {11,12}
       5 |  11 | {12}
       6 |  10 | {11,12}
       7 |  12 | {}
    (7 rows)

## See Also

- https://en.wikipedia.org/wiki/Transitive_closure
- The queries use the Sample Data network.

Indices and tables

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