Aggregating connected sets of nodes / edges - postgresql

Question

I have a connected set of edges with unique nodes. They are connected using a parent node. Consider the following example code and illustration:
CREATE TABLE network (
node integer PRIMARY KEY,
parent integer REFERENCES network(node),
length numeric NOT NULL
);
CREATE INDEX ON network (parent);
INSERT INTO network (node, parent, length) VALUES
(1, NULL, 1.3),
(2, 1, 1.2),
(3, 2, 0.9),
(4, 3, 1.4),
(5, 4, 1.6),
(6, 2, 1.5),
(7, NULL, 1.0);
Visually, two groups of edges can be identified. How can the two groups be identified using PostgreSQL 9.1, and length summed? The expected result is shown:
edges_in_group | total_edges | total_length
----------------+-------------+--------------
{1,2,3,4,5,6} | 6 | 7.9
{7} | 1 | 1.0
(2 rows)
I don't even know where to begin. Do I need a custom aggregate or window function? Could I use WITH RECURSIVE to iteratively collect edges that connect? My real world case is a stream network of 245,000 edges. I expect the maximum number of edges_in_group to be less than 200, and a couple hundred aggregated groups (rows).

Answer 1

A recursive query is the way to go:
with recursive tree as (
select node, parent, length, node as root_id
from network
where parent is null
union all
select c.node, c.parent, c.length, p.root_id
from network c
join tree p on p.node = c.parent
)
select root_id, array_agg(node) as edges_in_group, sum(length) as total_length
from tree
group by root_id;
The important thing is to keep the id of the root node in each recursion, so that you can group by that id in the final result.