pgr_lineGraph - Proposed

pgr_lineGraph — 将给定图转换为其相应的基于边的图。

Boost 图内部

Warning

下一版本的拟议功能。

• 它们并未正式出现在当前版本中。

• 它们可能会正式成为下一个版本的一部分：

  • 这些函数使用 ANY-INTEGER 和 ANY-NUMERICAL

  • 名字可能不会改变。（但仍然有可能改变）

  • 签名可能不会改变。（但仍然有可能改变）

  • 功能可能不会改变。（但仍然有可能改变）

  • pgTap 测试已经完成。 但可能需要更多。

  • 文档可能需要完善。

可用性

• Version 3.7.0

  • 晋升为 拟议 签名。

  • 适用于有向和无向图。

• 版本2.5.0

  • 新的 实验 函数

描述

Given a graph \(G\), its line graph \(L(G)\) is a graph such that:

• Each vertex of \(L(G)\) represents an edge of \(G\).

• Two vertices of \(L(G)\) are adjacent if and only if their corresponding edges share a common endpoint in \(G\)

主要特点是：

• 适用于有向和无向图。

• The cost and reverse_cost columns of the result represent existence of the edge.

• When the graph is directed the result is directed.

  • To get the complete Line Graph use unique identifiers on the double way edges (See Additional Examples).

• 当图无向时，成本矩阵是对称的。

  • The reverse_cost is always \(-1\).

签名

pgr_lineGraph(Edges SQL, [directed])

Returns set of (seq, source, target, cost, reverse_cost)

OR EMPTY SET

示例:

For an undirected graph with edges :math:'{2,4,5,8}'

SELECT * FROM pgr_lineGraph(
  'SELECT id, source, target, cost, reverse_cost
  FROM edges WHERE id IN (2,4,5,8)',
  false);
 seq | source | target | cost | reverse_cost
-----+--------+--------+------+--------------
   1 |      2 |      4 |    1 |           -1
   2 |      2 |      5 |    1 |           -1
   3 |      4 |      8 |    1 |           -1
   4 |      5 |      8 |    1 |           -1
(4 rows)

参数

参数	类型	描述
Edges SQL	TEXT	Edges SQL 如下所述。

可选参数

列	类型	默认	描述
directed	BOOLEAN	true	当 true 时，该图被视为有 有向 如果为 false ，则该图被视为 无向。

内部查询

Edges SQL

列	类型	默认	描述
id	ANY-INTEGER		边的标识符。
source	ANY-INTEGER		边的第一个端点顶点的标识符。
target	ANY-INTEGER		边的第二个端点顶点的标识符。
cost	ANY-NUMERICAL		边(source, target)的权重
reverse_cost	ANY-NUMERICAL	-1	边(target, source)的权重 当为负时：边（ target, source ）不存在，因此它不是图的一部分。

其中：

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

ANY-NUMERICAL:

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

结果列

Returns set of (seq, source, target, cost, reverse_cost)

列	类型	描述
seq	INTEGER	从 1 开始的顺序值。 给出边的本地标识符
source	BIGINT	当前边的源顶点的标识符。 为负时：源是原始图中的反向边。
target	BIGINT	当前边的目标顶点的标识符。 为负时：目标是原始图中的反向边。
cost	FLOAT	边 (source, target)的权重。 当为负时：边(source, target)不存在，因此它不是图的一部分。
reverse_cost	FLOAT	边 (target, source)的权重。 当为负时：边(target, source)不存在，因此它不是图的一部分。

其他示例

Given the following directed graph

\(G(V,E) = G(\{1,2,3,4\},\{ 1 \rightarrow 2, 1 \rightarrow 4, 2 \rightarrow 3, 3 \rightarrow 1, 3 \rightarrow 2, 3 \rightarrow 4, 4 \rightarrow 3\})\)

Representation as directed with shared edge identifiers

For the simplicity, the design of the edges table on the database, has the edge's identifiers are represented with 3 digits:

hundreds:

the source vertex

tens:

always 0, acts as a separator

units:

the target vertex

In this image,

• Single or double head arrows represent one edge (row) on the edges table.

• The numbers in the yellow shadow are the edge identifiers.

Two pair of edges share the same identifier when the reverse_cost column is used.

• Edges \({2 \rightarrow 3, 3 \rightarrow 2}\) are represented with one edge row with \(id=203\).

• Edges \({3 \rightarrow 4, 4 \rightarrow 3}\) are represented with one edge row with \(id=304\).

The graph can be created as follows:

CREATE TABLE edges_shared (
    id BIGINT,
    source BIGINT,
    target BIGINT,
    cost FLOAT,
    reverse_cost FLOAT,
    geom geometry
);
CREATE TABLE
INSERT INTO edges_shared (id, source, target, cost, reverse_cost, geom) VALUES
  (102, 1, 2, 1, -1, ST_MakeLine(ST_POINT(0,  2), ST_POINT(2,  2))),
  (104, 1, 4, 1, -1, ST_MakeLine(ST_POINT(0,  2), ST_POINT(0,  0))),
  (301, 3, 1, 1, -1, ST_MakeLine(ST_POINT(2,  0), ST_POINT(0,  2))),
  (203, 2, 3, 1,  1, ST_MakeLine(ST_POINT(2,  2), ST_POINT(2,  0))),
  (304, 3, 4, 1,  1, ST_MakeLine(ST_POINT(0,  0), ST_POINT(2,  0)));

Line Graph of a directed graph represented with shared edges

SELECT seq, source, target, cost, reverse_cost
FROM pgr_lineGraph(
  'SELECT id, source, target, cost, reverse_cost FROM edges_shared',
  true);
 seq | source | target | cost | reverse_cost
-----+--------+--------+------+--------------
   1 |    102 |    203 |    1 |           -1
   2 |    104 |    304 |    1 |           -1
   3 |    203 |    203 |    1 |            1
   4 |    203 |    301 |    1 |           -1
   5 |    203 |    304 |    1 |            1
   6 |    301 |    102 |    1 |           -1
   7 |    301 |    104 |    1 |           -1
   8 |    304 |    301 |    1 |           -1
   9 |    304 |    304 |    1 |            1
(9 rows)

• The result is a directed graph.

• For \(seq=4\) from \(203 \leftrightarrow 304\) represent two edges

• For all the other values of seq represent one edge.

• The cost and reverse_cost values represent the existence of the edge.

  • When positive: the edge exists.

  • When negative: the edge does not exist.

Representation as directed with unique edge identifiers

For the simplicity, the design of the edges table on the database, has the edge's identifiers are represented with 3 digits:

hundreds:

the source vertex

tens:

always 0, acts as a separator

units:

the target vertex

In this image,

• Single head arrows represent one edge (row) on the edges table.

• There are no double head arrows

• The numbers in the yellow shadow are the edge identifiers.

Two pair of edges share the same ending nodes and the reverse_cost column is not used.

• Edges \({2 \rightarrow 3, 3 \rightarrow 2}\) are represented with two edges \(id=203\) and \(id=302\) respectively.

• Edges \({3 \rightarrow 4, 4 \rightarrow 3}\) are represented with two edges \(id=304\) and \(id=403\) respectively.

The graph can be created as follows:

CREATE TABLE edges_unique (
    id BIGINT,
    source BIGINT,
    target BIGINT,
    cost FLOAT,
    geom geometry
);
CREATE TABLE
INSERT INTO edges_unique (id, source, target, cost, geom) VALUES
  (102, 1, 2, 1, ST_MakeLine(ST_POINT(0,  2), ST_POINT(2,  2))),
  (104, 1, 4, 1, ST_MakeLine(ST_POINT(0,  2), ST_POINT(0,  0))),
  (301, 3, 1, 1, ST_MakeLine(ST_POINT(2,  0), ST_POINT(0,  2))),
  (203, 2, 3, 1, ST_MakeLine(ST_POINT(2,  2), ST_POINT(2,  0))),
  (304, 3, 4, 1, ST_MakeLine(ST_POINT(2,  0), ST_POINT(0,  0))),
  (302, 3, 2, 1, ST_MakeLine(ST_POINT(2,  0), ST_POINT(2,  2))),
  (403, 4, 3, 1, ST_MakeLine(ST_POINT(0,  0), ST_POINT(2,  0)));

Line Graph of a directed graph represented with unique edges

SELECT seq, source, target, cost, reverse_cost
FROM pgr_lineGraph(
  'SELECT id, source, target, cost FROM edges_unique',
  true);
 seq | source | target | cost | reverse_cost
-----+--------+--------+------+--------------
   1 |    102 |    203 |    1 |           -1
   2 |    104 |    403 |    1 |           -1
   3 |    203 |    301 |    1 |           -1
   4 |    203 |    304 |    1 |           -1
   5 |    301 |    102 |    1 |           -1
   6 |    301 |    104 |    1 |           -1
   7 |    302 |    203 |    1 |            1
   8 |    304 |    403 |    1 |            1
   9 |    403 |    301 |    1 |           -1
  10 |    403 |    302 |    1 |           -1
(10 rows)

• The result is a directed graph.

• For \(seq=7\) from \(203 \leftrightarrow 302\) represent two edges.

• For \(seq=8\) from \(304 \leftrightarrow 403\) represent two edges.

• For all the other values of seq represent one edge.

• The cost and reverse_cost values represent the existence of the edge.

  • When positive: the edge exists.

  • When negative: the edge does not exist.

另请参阅

• wikipedia: Line Graph

• mathworld: Line Graph

• 示例数据

索引和表格

• Index

• Search Page