Yes you can store the relation in one table.
Then you can self join(inner or left)
depending upon the requirement.
declare @Father table(id int,name,FatherID int)
insert into @Father values(1,'John',null),(2,'Peter',1)
Let me know what else is your requirement related to it.
Sorry now I understood your question . I was thinking it as Employee- Manager Relation.
So from Employee- Manager Relation point of view my design is correct.If same Father can be child of another person.
In fact now you have to give some more example.
You are thinking in this manner
declare @Father table(id int identity(1,1),FatherName varchar(50),ChildName varchar(50))
insert into @Father values ('John','pqr')
Can you populate record as per your requirement ?