I am currently working with a weighted adjacency matrix for a directed graph, and it contains several 0 columns and rows.  With the unaltered matrix, I am able to monitor the relations between vertices with,

This outputs a table with the corresponding vertex list labeling the rows and columns.  I want to delete the 0 rows and columns while altering the labels to reflect the change.  My matrix is currently $85\times 85$, and eliminating the necessary rows and columns reduces the size to $77\times 38$. I could theoretically go through by hand and track the eliminated entries, but that sounds way too time consuming for something that I'm sure has a simple solution.  Any help is appreciated. 

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