Owing to their potential for systematic analysis, complex networks have been widely used in proteomics. Representing a protein structure as a topology network provides novel insight into understanding protein folding mechanisms, stability and function. Here, we develop a new feature to reveal correlations between residues using a protein structure network. In an original attempt to quantify the effects of several key residues on catalytic residues, a power function was used to model interactions between residues. The results indicate that focusing on a few residues is a feasible approach to identifying catalytic residues. The spatial environment surrounding a catalytic residue was analyzed in a layered manner. We present evidence that correlation between residues is related to their distance apart most environmental parameters of the outer layer make a smaller contribution to prediction and ii catalytic residues tend to be located near key positions in enzyme folds. Feature analysis revealed satisfactory performance for our features, which were combined with several conventional features in a prediction model for catalytic residues using a comprehensive data set from the Catalytic Site Atlas. Values of 88.6 for sensitivity and 88.4 for specificity were obtained by 10-fold cross-validation. These results suggest that these features reveal the mutual dependence of residues and are promising for further study of structure-function relationship.