Graph Hierarchy: What Is It Exactly?!!

Dec 21, 2007

Hi everybody,
I've been reading the book MCITP Self-Paced Training Kit (Exam 70-441): Designing Database Solutions by Using Microsoft SQL Server(TM) 2005 (Self-Paced Training Kits) as a part of my preparation for exam 70-441
The book is really clear, and I could understand everything easily because I've some experience as a database developer.
Until now, there's only one thing that I didn't fully understand:
On pages 53 and 54, it mentions a type of hierarchy called: a graph hierarchy, and it gives a small example made the things even more complicated
I've many books about database design theories, but they don't use the term (graph hierarchy) any where...
So, I appreciate if you can point me to an online resource or a book that discusses this term thorougly.

Thank you

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if object_id('g3')>0 drop table g3
if object_id('g3x')>0 drop table g3x
if object_id('g3y')>0 drop table g3y
if object_id('g3l')>0 drop table g3l
GO
create table g3y(v1 int, v2 int) -- ancillary table
GO
create table g3x(n int, v1 int, v2 int) -- ancillary table
GO
create table g3l(nl int, v1 int, v2 int)
-- table for storing of 'detected' loops
GO
create table g3(v1 int, v2 int)
-- table of test data with pairs of adjoining vertexes
-- each vertex is named by an arbitrary number
GO
insert into g3
select 2, 3 union all
select 2, 4 union all
select 1, 4 union all
select 3, 5 union all
select 5, 6 union all
select 1, 6 union all
select 4, 7 union all
select 6, 8 union all
select 3, 9 union all
select 1, 7 union all
select 2, 7 union all
select 1, 8 union all
select 5, 8 union all
select 2, 9 union all
select 5, 9 ----union all
/*
select 2, 13 union all
select 3, 13 union all
select 13, 14 union all
select 12, 14 union all
select 12, 15 union all
select 11, 15 union all
select 11, 13 union all
select 10, 11 union all
select 10, 12 union all
select 10, 14 union all
select 10, 15
*/
GO
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declare @i int, @n int, @v1 int, @v2 int
set @i=1

while 0=0
begin
set @n=1
truncate table g3x truncate table g3y
select top 1 @v1=g3.v1, @v2=g3.v2 from g3 left join g3l on
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insert into g3x select @n, @v1, @v2

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begin
set @n=@n+1
insert into g3x select top 1 @n, v1, v2 from g3 where v2=@v1
and v1<>@v2 and v1=(select top 1 v2 from g3x order by n desc)

if @@rowcount=0
begin
insert into g3x select top 1 @n, v1, v2 from g3 where
v2 not in (select v1 from g3x union all select v2 from g3x) and
v1=(select top 1 v2 from g3x order by n desc) and not exists
(select 0 from g3y where g3y.v1=g3.v1 and g3y.v2=g3.v2)
if @@rowcount=0
if @n>2
begin
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delete from g3x where n=@n-1
set @n=@n-2
end
else
begin insert into g3l select 0, v1, v2 from g3x break end
end
else
begin
insert into g3l select @i, v1, v2 from g3x set @i=@i+1
end
end
end
select * from g3l order by nl
Below is what we get:

nl v1 v2
----------- ----------- -----------
1 2 3
1 3 5
1 5 6
1 6 8
1 8 1
1 1 4
1 4 2

2 1 6
2 6 8
2 8 1

3 4 7
3 7 1
3 1 4

4 3 9
4 9 2
4 2 3

5 2 7
5 7 4
5 4 2

6 5 8
6 8 6
6 6 5

7 5 9
7 9 3
7 3 5
Of course, in general case not all found by the code loops are minimal.
But this is exactly my approach:
firstly find any possible loops (avoiding excessiveness!!),
then, in WHILE loop, try to mark out minimal loop(s) from intersection of
two non-minimal loops... seems it will be an interesting t-sql job.

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