# pgr_connectedComponents¶

pgr_connectedComponents — Componentes conectados de un grafo no dirigido mediante un enfoque basado en DFS.

• Versión 3.0.0

• Las columnas de retorno cambian:

• n_seq se elimina

• seq cambió el tipo a BIGINT

• Función oficial

• Versión 2.5.0

• Nueva función experimental

## Descripción¶

Un componente conectado de un gráfico no direccionado es un conjunto de vértices que son todos accesibles entre sí.

Las principales características son:

• Funciona para grafos no dirigidos.

• Los componentes se describen mediante vértices

• Los valores regresados se ordenan:

• component ascendente

• node ascendente

• Tiempo de ejecución: $$O(V + E)$$

## Firmas¶

pgr_connectedComponents(Edges SQL)
RETURNS SET OF (seq, component, node)
OR EMPTY SET
Ejemplo:

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



## Parámetros¶

Parámetro

Tipo

Descripción

SQL Aristas

TEXT

## Consultas Internas¶

### SQL aristas¶

Columna

Tipo

x Defecto

Descripción

id

ENTEROS

source

ENTEROS

Identificador del primer vértice de la arista.

target

ENTEROS

Identificador del segundo vértice de la arista.

cost

FLOTANTES

Peso de la arista (source, target)

reverse_cost

FLOTANTES

-1

Peso de la arista (target, source)

• Cuando negativo: la arista (target, source) no existe, por lo tanto no es parte del grafo.

Donde:

ENTEROS:

SMALLINT, INTEGER, BIGINT

FLOTANTES:

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Returns set of (seq, component, node)

Columna

Tipo

Descripción

seq

BIGINT

Valor secuencial a partir de 1.

component

BIGINT

• Continene le valor mínimo de identificador de nodo en el componente.

node

BIGINT

Identificador del vértice que pertenece al component.

Para obtener la conectividad del grafo:

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



In this example, the component $$2$$ consists of vertices $$\{2, 4\}$$ and both vertices are also part of the dead end result set.

This graph needs to be connected.

Nota

With the original graph of this documentation, there would be 3 components as the crossing edge in this graph is a different component.

#### Prepare storage for connection information¶

ALTER TABLE vertices ADD COLUMN component BIGINT;
ALTER TABLE
ALTER TABLE edges ADD COLUMN component BIGINT;
ALTER TABLE


#### Save the vertices connection information¶

UPDATE vertices SET component = c.component
FROM (SELECT * FROM pgr_connectedComponents(
'SELECT id, source, target, cost, reverse_cost FROM edges'
)) AS c
WHERE id = node;
UPDATE 18


#### Save the edges connection information¶

UPDATE edges SET component = v.component
FROM (SELECT id, component FROM vertices) AS v
WHERE source = v.id;
UPDATE 20


#### Get the closest vertex¶

Using pgr_findCloseEdges the closest vertex to component $$1$$ is vertex $$4$$. And the closest edge to vertex $$4$$ is edge $$14$$.

SELECT edge_id, fraction, ST_AsText(edge) AS edge, id AS closest_vertex
FROM pgr_findCloseEdges(
$$SELECT id, geom FROM edges WHERE component = 1$$,
(SELECT array_agg(geom) FROM vertices WHERE component = 2),
2, partial => false) JOIN vertices USING (geom) ORDER BY distance LIMIT 1;
edge_id | fraction |                 edge                 | closest_vertex
---------+----------+--------------------------------------+----------------
14 |      0.5 | LINESTRING(1.999999999999 3.5,2 3.5) |              4
(1 row)



The edge can be used to connect the components, using the fraction information about the edge $$14$$ to split the connecting edge.

#### Conectando componentes¶

There are three basic ways to connect the components

• From the vertex to the starting point of the edge

• From the vertex to the ending point of the edge

• From the vertex to the closest vertex on the edge

• This solution requires the edge to be split.

The following query shows the three ways to connect the components:

WITH
info AS (
SELECT
edge_id, fraction, side, distance, ce.geom, edge, v.id AS closest,
source, target, capacity, reverse_capacity, e.geom AS e_geom
FROM pgr_findCloseEdges(
$$SELECT id, geom FROM edges WHERE component = 1$$,
(SELECT array_agg(geom) FROM vertices WHERE component = 2),
2, partial => false) AS ce
JOIN vertices AS v USING (geom)
JOIN edges AS e ON (edge_id = e.id)
ORDER BY distance LIMIT 1),
three_options AS (
SELECT
closest AS source, target, 0 AS cost, 0 AS reverse_cost,
capacity, reverse_capacity,
ST_X(geom) AS x1, ST_Y(geom) AS y1,
ST_X(ST_EndPoint(e_geom)) AS x2, ST_Y(ST_EndPoint(e_geom)) AS y2,
ST_MakeLine(geom, ST_EndPoint(e_geom)) AS geom
FROM info

UNION

SELECT closest, source, 0, 0, capacity, reverse_capacity,
ST_X(geom) AS x1, ST_Y(geom) AS y1,
ST_X(ST_StartPoint(e_geom)) AS x2, ST_Y(ST_StartPoint(e_geom)) AS y2,
ST_MakeLine(info.geom, ST_StartPoint(e_geom))
FROM info
/*
UNION
-- This option requires splitting the edge
SELECT closest, NULL, 0, 0, capacity, reverse_capacity,
ST_X(geom) AS x1, ST_Y(geom) AS y1,
ST_X(ST_EndPoint(edge)) AS x2, ST_Y(ST_EndPoint(edge)) AS y2,
edge
FROM info */
)

INSERT INTO edges
(source, target,
cost, reverse_cost,
capacity, reverse_capacity,
x1, y1, x2, y2,
geom)
(SELECT
source, target, cost, reverse_cost, capacity, reverse_capacity,
x1, y1, x2, y2, geom
FROM three_options);
INSERT 0 2


#### Checking components¶

Ignoring the edge that requires further work. The graph is now fully connected as there is only one component.

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



Índices y tablas