# pgr_maxCardinalityMatch¶

pgr_maxCardinalityMatch — Calculates a maximum cardinality matching in a graph.

Availability

• Version 3.0.0

• Official function

• Version 2.5.0

• Renamed from pgr_maximumCardinalityMatching

• Proposed function

• Version 2.3.0

• New Experimental function

## Description¶

The main characteristics are:

• A matching or independent edge set in a graph is a set of edges without common vertices.

• A maximum matching is a matching that contains the largest possible number of edges.

• There may be many maximum matchings.

• Calculates one possible maximum cardinality matching in a graph.

• The graph can be directed or undirected.

• Running time: $$O( E*V * \alpha(E,V))$$

## Signatures¶

pgr_maxCardinalityMatch(Edges SQL [, directed])

RETURNS SET OF (seq, edge_id, source, target)
OR EMPTY SET
Example:

For a directed graph

SELECT * FROM pgr_maxCardinalityMatch(
'SELECT id, source, target, cost AS going, reverse_cost AS coming
FROM edges');
seq | edge | source | target
-----+------+--------+--------
1 |    6 |      1 |      3
2 |   17 |      2 |      4
3 |    1 |      5 |      6
4 |   14 |      8 |      9
5 |    9 |     11 |     16
6 |   13 |     12 |     17
7 |   18 |     13 |     14
8 |    3 |     15 |     10
(8 rows)



## Inner Queries¶

### Edges SQL¶

SQL query, which should return a set of rows with the following columns:

Column

Type

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.

going

ANY-NUMERIC

A positive value represents the existence of the edge (source, target).

coming

ANY-NUMERIC

A positive value represents the existence of the edge (target, source).

Where:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

ANY-NUMERIC:

SMALLINT, INTEGER, BIGINT, REAL FLOAT

## Result Columns¶

Column

Type

Description

seq

INT

Sequential value starting from 1.

edge

BIGINT

Identifier of the edge in the original query.

source

BIGINT

Identifier of the first end point of the edge.

target

BIGINT

Identifier of the second end point of the edge.