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Mar 28, 2010 at 23:05 comment added user4977 Thanks. It is nice to know that the matrix is actually commonly referred to as the weighted adjacency matrix, as that is what I have been calling it. The literature I am familiar with on the topic (which is all in the realm of modeling transportation systems) seems to define the graph from the matrix, never the other way around, so it gives no name to the matrix. To address your comment, I personally don't want anything else from the matrix, but I didn't want to exclude the possibility that there was another natural and useful matrix to represent a weighted digraph.
Mar 28, 2010 at 21:27 history answered Ryan Williams CC BY-SA 2.5