Is this transitive closure correct or not?

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Natalie1
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Could you explain what you mean by the table and especially by the column next to it?
 
It is an Adjacency matrix, on the right side is a direct transitive closure. Explain to me why the first one is 0, second - 1, third - 2 etc. I don't understand this transitive closure.
 
Natalie said:
It is an Adjacency matrix, on the right side is a direct transitive closure.
Transitive closure of a relation is another relation. It can be represented by its own adjacency matrix, but I don't understand how it is represented by a column.