declare @graph table (parent bigint not NULL, child bigint not NULL, [weight] int not NULL, gID bigint, max_lvl int, primary key(parent, child, [weight]), unique(child, parent, [weight]) );
declare @gID bigint;

insert into @graph(parent, child, [weight])
Values 
-- 1 граф
(1, 1, 1), (1, 2, 1), (1, 3, 10), (2, 3, 2), (3, 1, 3), (3, 6, 1), (6, 6, 2)
-- 2 граф
, (4, 4, 1), (4, 5, 1), (5, 4, 2), (5, 4, 1);

--	1.
;with cte as (
	select
		start_node  =parent
		,node		=child
		,[path]		=cast('/'+cast(parent as varchar(10))+'/'+cast(child as varchar(10))+'/' as varchar(max))
		,lvl		=1 
	from @graph 
	--where parent<>child

	union all

	select 
		cte.start_node
		,node	=t.child
		,[path]	=cast(cte.[path]+cast(t.child as varchar(10))+'/' as varchar(max))
		,lvl	=cte.lvl+1 
	from @graph t inner join cte on t.parent=cte.node
	where cte.[path] not like '%/'+cast(t.child as varchar(10))+'/%'
),
cte1 as 
	(select start_node, max(lvl) as max_lvl from cte group by start_node)

update a 
set a.max_lvl	=b.max_lvl
from @graph a inner join cte1 b on a.parent=b.start_node

--	2.
set @gID = 1
while 1=1 begin
	;with cte as 
		(select top 1 parent, gID from @graph where gID is null order by max_lvl desc)
	update cte set gID=@gID

	if @@ROWCOUNT = 0 break;

	while 1=1 begin
		;with cte as 
			(select parent as node from @graph where gID=@gID union select child as node from @graph where gID=@gID)
		update @graph
		set gID=@gID
		where	gID is null
			and (parent in (select node from cte) or child in (select node from cte))

		if @@ROWCOUNT = 0 break;				
	end

	set @gID = @gID + 1
end

--	result
;with cte as 
	(select *, row_number()over(partition by gID order by [weight] desc) as rn from @graph)

select distinct  
	b.gID
	,b.parent
	,a.child
	,b.[weight] as max_weight
from @graph a inner join cte b on a.gID=b.gID
where b.rn=1