 # pgr_contractGraph - Proposed¶

pgr_contractGraph — Performs graph contraction and returns the contracted vertices and edges.

Warning

These are proposed 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

## Synopsis¶

Contraction reduces the size of the graph by removing some of the vertices and edges and, for example, might add edges that represent a sequence of original edges decreasing the total time and space used in graph algorithms.

## Characteristics¶

The main Characteristics are:
• Process is done only on edges with positive costs.
• There are two types of contraction methods used namely,
• Dead End Contraction
• Linear Contraction
• The values returned include the added edges and contracted vertices.
• The returned values are ordered as follows:
• column id ascending when type = v
• column id descending when type = e

## Signature Summary:¶

The pgr_contractGraph function has the following signatures:

pgr_contractGraph(edges_sql, contraction_order)
pgr_contractGraph(edges_sql, contraction_order, max_cycles, forbidden_vertices, directed)

RETURNS SETOF (seq, type, id, contracted_vertices, source, target, cost)


## Signatures¶

### Minimal signature¶

pgr_contractGraph(edges_sql, contraction_order)

Example: Making a dead end contraction and a linear contraction.
SELECT * FROM pgr_contractGraph(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[1, 2]);
seq | type | id | contracted_vertices | source | target | cost
-----+------+----+---------------------+--------+--------+------
1 | v    |  5 | {7,8}               |     -1 |     -1 |   -1
2 | v    | 15 | {14}                |     -1 |     -1 |   -1
3 | v    | 17 | {16}                |     -1 |     -1 |   -1
4 | e    | -1 | {1,2}               |      3 |      5 |    2
5 | e    | -2 | {4}                 |      9 |      3 |    2
6 | e    | -3 | {10,13}             |      5 |     11 |    2
7 | e    | -4 | {12}                |     11 |      9 |    2
(7 rows)


### Complete signature¶

pgr_contractGraph(edges_sql, contraction_order, max_cycles, forbidden_vertices, directed)

Example: Making a dead end contraction and a linear contraction and vertex 2 is forbidden from contraction
SELECT * FROM pgr_contractGraph(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[1, 2], forbidden_vertices:=ARRAY);
seq | type | id | contracted_vertices | source | target | cost
-----+------+----+---------------------+--------+--------+------
1 | v    |  2 | {1}                 |     -1 |     -1 |   -1
2 | v    |  5 | {7,8}               |     -1 |     -1 |   -1
3 | v    | 15 | {14}                |     -1 |     -1 |   -1
4 | v    | 17 | {16}                |     -1 |     -1 |   -1
5 | e    | -1 | {4}                 |      9 |      3 |    2
6 | e    | -2 | {10,13}             |      5 |     11 |    2
7 | e    | -3 | {12}                |     11 |      9 |    2
(7 rows)


### Description of the edges_sql query¶

edges_sql: an SQL query, which should return a set of rows with the following columns:
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 SMALLINT, INTEGER, BIGINT, REAL, FLOAT

## Description of the parameters of the signatures¶

Column Type Description
edges_sql TEXT SQL query as described above.
contraction_order ARRAY[ANY-INTEGER]
Ordered contraction operations.
• 1 = Dead end contraction
• 2 = Linear contraction
forbidden_vertices ARRAY[ANY-INTEGER] (optional). Identifiers of vertices forbidden from contraction. Default is an empty array.
max_cycles INTEGER (optional). Number of times the contraction operations on contraction_order will be performed. Default is 1.
directed BOOLEAN
• When true the graph is considered as Directed.
• When false the graph is considered as Undirected.

## Description of the return values¶

RETURNS SETOF (seq, type, id, contracted_vertices, source, target, cost)

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

Column Type Description
seq INTEGER Sequential value starting from 1.
type TEXT
Type of the id.
• ‘v’ when id is an identifier of a vertex.
• ‘e’ when id is an identifier of an edge.
id BIGINT
Identifier of:
• the vertex when type = ‘v’.
• The vertex belongs to the edge_table passed as a parameter.
• the edge when type = ‘e’.
• The id is a decreasing sequence starting from -1.
• Representing a pseudo id as is not incorporated into the edge_table.
contracted_vertices ARRAY[BIGINT] Array of contracted vertex identifiers.
source BIGINT Identifier of the source vertex of the current edge id. Valid values when type = ‘e’.
target BIGINT Identifier of the target vertex of the current edge id. Valid values when type = ‘e’.
cost FLOAT Weight of the edge (source, target). Valid values when type = ‘e’.

# Examples¶

Example: Only dead end contraction
SELECT * FROM pgr_contractGraph(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY);
seq | type | id | contracted_vertices | source | target | cost
-----+------+----+---------------------+--------+--------+------
1 | v    |  2 | {1}                 |     -1 |     -1 |   -1
2 | v    |  5 | {7,8}               |     -1 |     -1 |   -1
3 | v    | 10 | {13}                |     -1 |     -1 |   -1
4 | v    | 15 | {14}                |     -1 |     -1 |   -1
5 | v    | 17 | {16}                |     -1 |     -1 |   -1
(5 rows)

Example: Only linear contraction
SELECT * FROM pgr_contractGraph(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY);
seq | type | id | contracted_vertices | source | target | cost
-----+------+----+---------------------+--------+--------+------
1 | e    | -1 | {4}                 |      9 |      3 |    2
2 | e    | -2 | {8}                 |      5 |      7 |    2
3 | e    | -3 | {8}                 |      7 |      5 |    2
4 | e    | -4 | {12}                |     11 |      9 |    2
(4 rows)


Indices and tables