Fastest way to traverse all edge of a directed attributed graph which stores in adjacency matrix

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I have a adjacency matrix which represent a directed attributed graph. Now I want to traverse all of the edge of the graph. One way is too traverse all rows of the matrix but my problem is that when the number of rows are more than 10000 the performance of traversing edges degrade significantly. So I want to know is there any efficient way to do that?

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