  A protein structure is represented as a network of residues whereby edges are
determined by intra-molecular contacts. We introduce inhomogeneity into these
networks by assigning each edge a weight that is determined by amino-acid pair
potentials. Two methodologies are utilized to calculate the average path
lengths (APLs) between pairs: To minimize (i) the maximum weight in the strong
APL, and (ii) the total weight in the weak APL. We systematically screen edges
that have higher than a cutoff potential and calculate the shortest APLs in
these reduced networks, while keeping chain connectivity. Therefore,
perturbations introduced at a selected region of the residue network propagate
to remote regions only along the non-screened edges that retain their ability
to disseminate the perturbation. The shortest APLs computed from the reduced
homogeneous networks with only the strongest few non-bonded pairs closely
reproduce the strong APLs from the weighted networks. The rate of change in the
APL in the reduced residue network as compared to its randomly connected
counterpart remains constant until a lower bound. Upon further link removal,
this property shows an abrupt increase, towards a random coil behavior. Under
different perturbation scenarios, diverse optimal paths emerge for robust
residue communication.
