SQL Server 2017

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create table tbl_nodes
(
    nod1 varchar(50),
    nod2 varchar(50),
    nod_length float
);
insert into tbl_nodes values('A','B',1600); 
insert into tbl_nodes values('G','H',45000);
insert into tbl_nodes values('B','C',2300);
insert into tbl_nodes values('C','D',2640);
insert into tbl_nodes values('B','D',2840);
insert into tbl_nodes values('C','E',2940);
insert into tbl_nodes values('D','F',2340);
insert into tbl_nodes values('M','N',9000);
insert into tbl_nodes values('E','A',100000);
9 rows affected

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, '_%'))


nodes
total_length


-A-B-D-F-
6780

-A-B-C-E-
6840

-A-B-C-D-F-
8880