I have the following table with sample data:
Table: tbl_nodes
create table tbl_nodes
(
nod1 varchar(50),
nod2 varchar(50),
n
I'm pretty sure you need a recursive CTE. However, your sample results doesn't make sense.
The following basically does what you want:
with cte AS (
select nod1, nod2, nod_length as Total_length,
convert(varchar(max), concat('-', nod1, '-', nod2, '-')) as nodes, 1 as lev
from tbl_nodes n
where nod1 = 'A'
union all
select cte.nod1, n.nod2, cte.Total_length + n.nod_length,
convert(varchar(max), concat(cte.nodes, n.nod2, '-')) as nodes, lev + 1
from cte join
tbl_nodes n
on cte.nod2 = n.nod1
where nodes not like concat('%-', n.nod2, '-%')
)
select nodes, total_length
from cte
where not exists (select 1
from cte cte2
where cte2.nodes like concat(cte.nodes, '_%')
);
Here is a db<>fiddle.