Finding All Minimal Cyclic Paths In The Graph

Here a code for finding all minimal loops (cyclic paths) in a graph
with vertexes of degree >= 3. Almost obviously that before seeking
for loops we should eliminate from the graph all its vertexes of degree < 3
(degree of a vertex is the number of edges outcoming from the vertex).
Note: there are no any 'parent' - 'child' nodes here. All vertexes are
absolutely equitable.
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
insert into g3 select v2, v1 from g3

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
(g3.v1=g3l.v1 and g3.v2=g3l.v2)or(g3.v1=g3l.v2 and g3.v2=g3l.v1)
where g3l.nl is null if @@rowcount=0 break
insert into g3x select @n, @v1, @v2

while @v1<>(select top 1 v2 from g3x order by n desc)
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
insert into g3y select v1, v2 from g3x where n=@n-1
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.