Before revision:  Shannon entropy of information transport between two residues along a shortest path is lower than the entropies along longer paths between the same two points leading to the conclusion that communication over shortest paths results in highest lossless encoding .
After revision:  The shortest path residues are the highly visited residues during information transport. These paths are shown to lie on the high entropy landscape of the protein where entropy is taken to increase with abundance of visits to nodes during signal transport .