# pgRouting Manual (3.3)

## pgr_bipartite -Experimental

- Supported versions: Latest (3.3) 3.2

# pgr_bipartite -Experimental

`pgr_bipartite` — If graph is bipartite then function returns the vertex id along with color (0 and 1) else it will return an empty set. In particular, the is_bipartite() 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 3.2.0

  - New experimental function

## 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

  The pgr_bipartite algorithm with and edge_sql as a parameter when graph is bipartite:

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

## Parameters

Parameter | Type | Description
--- | --- | ---
Edges SQL | `TEXT` | Inner query as described below.

## Inner query

Edges SQL

  an SQL query of an undirected graph, 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`

- When positive: edge (source, target) exist on the graph.

- When negative: edge (source, target) does not exist on the graph.

reverse_cost

`ANY-NUMERICAL`

-1

- When positive: edge (target, source) exist on the graph.

- When negative: edge (target, source) does not exist on 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.

## Additional Example

Example

  The odd length cyclic graph can not be bipartite.

The following edge will make subgraph with vertices {1, 2, 5, 7, 8} an odd length cyclic graph.

    INSERT INTO edge_table (source, target, cost, reverse_cost) VALUES
    (1, 7, 1, 1);
    INSERT 0 1

The new graph is not bipartite because it has a odd length cycle of 5 vertices. Edges in blue represent odd length cycle.

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

## See Also

- Boost: is_bipartite algorithm documentation

- Wikipedia: bipartite graph

- Sample Data network.

Indices and tables

- Index

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