Evolutionarily conserved hydrophobic residues at the core of protein structures are generally assumed to play a structural role in protein folding and stability. Recent studies have implicated that their importance to protein structures is uneven, with a few of them being crucial and the rest of them being secondary. In this work, we explored the possibility of employing this feature of native structures for discriminating non-native structures from native ones. First, we developed a network tool to quantitatively measure the structural contributions of individual amino acid residues. We systematically applied this method to diverse fold-type sets of native proteins. It was confirmed that this method could grasp the essential structural features of native proteins. Next, we applied it to a number of decoy sets of proteins. The results indicate that such an approach indeed identified non-native structures in most test cases. This finding should be of help for the investigation of the fundamental problem of protein structure prediction.