The three dimensional structure of a protein is an outcome of the interactions of its constituent amino acids in 3D space. Considering the amino acids as nodes and the interactions among them as edges we have constructed and analyzed protein contact networks at different length scales, long and short-range. While long and short-range interactions are determined by the positions of amino acids in primary chain, the contact networks are constructed based on the 3D spatial distances of amino acids. We have further divided these networks into sub-networks of hydrophobic, hydrophilic and charged residues. Our analysis reveals that a significantly higher percentage of assortative sub-clusters of long-range hydrophobic networks helps a protein in communicating the necessary information for protein folding in one hand; on the other hand the higher values of clustering coefficients of hydrophobic sub-clusters play a major role in slowing down the process so that necessary local and global stability can be achieved through intra connectivities of the amino acid residues. Further, higher degrees of hydrophobic long-range interactions suggest their greater role in protein folding and stability. The small-range all amino acids networks have signature of hierarchy. The present analysis with other evidences suggest that in a protein's 3D conformational space, the growth of connectivity is not evolved either through preferential attachment or through random connections; rather, it follows a specific structural necessity based guiding principle - where some of the interactions are primary while the others, generated as a consequence of these primary interactions are secondary.