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Can any one please tell me if this matrix is correct also how to i simplify further more? Thanks.

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The row for 9 shows things that are not in the column for 9. That's all I see. If you want to simplify it, just remove the matrix under the diagonal like in your other example.

And graphs with arrows are called directed graphs, not direct. You only use them if it makes sense for the edges to go only one direction (like one-way streets).
mustish1Author Commented:
9 only connects with node 5 and node 7
mustish1Author Commented:
Can you also please tell me how these values came in that table from the first one?

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