What are you trying to do?
Considering the (common?) case of a 2-manifold mesh the number of edges is actually O(number of vertices). So storing the adj. matrix seems like a waste of space. Consider adj. lists instead.
If you are interested in the connectivity of your mesh (eg. what are the adj. faces of this edge, loop through all edges of a face...) there
are more suitable data structures like the half edge DS.
If you really need the adj. matrix, ignore this post.