This book presents a study of structural properties of proteins, with an exceptional finding and its correlation to folding kinetics. Proteins, with their structure-specific functions, form an important class of biomolecules for cellular functions. I used a coarse-grained graph theoretical approach, also known as complex network analysis, for my investigations. This methodology has been applied to study many complex systems ranging from social networks, technological networks (internet, WWW), transportation networks and biological networks (macromolecular, brain functional networks etc.). Interestingly, these systems with disparate origins and nature have been found to have certain common network features. In my investigations I uncovered an exceptional, generic property ("assortativity") of network models of proteins structures. I built contact networks of protein structure at different interaction-scales to identify biophysical correlate of assortativity. These findings reiterate the importance of coarse-grained models in understanding the function, kinetics of proteins. This modeling paradigm could be crucial for protein folding problem and for targeted design of enzymes.