Given a graph G (V, E), a labeling ∂: V ∪ E → {1,2...k} is called an edge irregular total k-labeling if for every pair of distinct edges uv and xy, ∂(u) + ∂(uv) + ∂(v) ≠ ∂(x) + ∂(y) + ∂(xy). The minimum k for which G has an edge irregular total k-labeling is called the total edge irregularity strength of G. In this paper we examine the total edge irregularity strength of the butterfly and the benes network. © 2011 Springer-Verlag.