I removed  The modified adjacency matrix is generated by replacing all entries greater than 1 in the adjacency matrix by 1.  from the article. The edges in graphs are defined as a set, so it is not possible that an edge (vi,vj) is contained more than once. I think the adjacency matrix should be a (0,1)-matrix and perhaps in a subsection someone could extend this definition to count the number of edges two vertices share. 