The three-dimensional structure of a protein can be described as a graph where nodes represent residues and interactions between them are edges. We have constructed protein contact networks at different length-scales for different interaction strength cutoffs. The largest connected component of short-range networks exhibit a highly cooperative transition, while long- and all-range networks (more similar to each other), have less cooperativity. The hydrophobic subnetworks in all- and long-range networks have similar phase transition behaviours while hydrophilic and charged networks don't. Hydrophobic subclusters in long- and all-range networks exhibit higher occurrence of assortativity and hence higher communication ability in transmitting information within a protein. The highly cliquish hydrophobic nodes in long- and short-range networks play a significant role in bridging and stabilizing distantly placed residues during protein folding. We have also observed a significant dominance of charged residues cliques in short-range networks. © 2012 Springer-Verlag.