Alignment and comparison of protein 3D structures is an important and fundamental task in structural biology to study evolutionary, functional and structural relatedness among proteins. Since two decades, the research on protein structure alignment has been taken up on priority and numbers of research articles are being published. There are incremental advances over previous efforts, and still these methods continue to improve over the time and still this is an open problem in structural biology. A novel methodology has been developed for comparing protein 3D structure by employing conversion of pair of protein 3D structures into 2D graphs (undirected weighted graph), partitioning of 2D graphs into sub-graphs, matching sub-graphs with main graphs and finally these sub-graphs matches calculates similarity between the pair of proteins. The proposed method has been implemented in MATLAB and R Package. The performance of the developed methodology is tested with four existing best methods such as CE, jFATCAT, TM_Align and Dali on 100 proteins benchmark dataset with SCOP database. The proposed method is efficient in terms of time complexity, accuracy, grouping of proteins in relevant structural groups and provides additional information towards non-bonded interactions and sub-graphs indicates the dominance of secondary structure.