# pgr_bipartite -Experimental¶

pgr_bipartite — Disjoint sets of vertices such that no two vertices within the same set are adjacent.

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 3.2.0

• New experimental signature

## Description¶

A bipartite graph is a graph with two sets of vertices which are connected to each other, but not within themselves. A bipartite graph is possible if the graph coloring is possible using two colors such that vertices in a set are colored with the same color.

The main Characteristics are:

• The algorithm works in undirected graph only.

• The returned values are not ordered.

• The algorithm checks graph is bipartite or not. If it is bipartite then it returns the node along with two colors 0 and 1 which represents two different sets.

• If graph is not bipartite then algorithm returns empty set.

• Running time: $$O(V + E)$$

## Signatures¶

pgr_bipartite(Edges SQL)
RETURNS SET OF (vertex_id, color_id)
OR EMPTY SET
Example:

When the graph is bipartite

SELECT * FROM pgr_bipartite(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$
) ORDER BY vertex_id;
vertex_id | color_id
-----------+----------
1 |        0
2 |        0
3 |        1
4 |        1
5 |        0
6 |        1
7 |        0
8 |        1
9 |        0
10 |        0
11 |        1
12 |        0
13 |        0
14 |        1
15 |        1
16 |        0
17 |        1
(17 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 (vertex_id, color_id)

Column

Type

Description

vertex_id

BIGINT

Identifier of the vertex.

color_id

BIGINT

Identifier of the color of the vertex.

• The minimum value of color is 1.

Example:

The odd length cyclic graph can not be bipartite.

The edge $$5 \rightarrow 1$$ will make subgraph with vertices $$\{1, 3, 7, 6, 5\}$$ an odd length cyclic graph, as the cycle has 5 vertices.

INSERT INTO edges (source, target, cost, reverse_cost) VALUES
(5, 1, 1, 1);
INSERT 0 1


Edges in blue represent odd length cycle subgraph.

SELECT * FROM pgr_bipartite(
$$SELECT id, source, target, cost, reverse_cost FROM edges$$
);
vertex_id | color_id
-----------+----------
(0 rows)