The study of functional residues (FRs) is essential for understanding protein functions and biological processes. The amino acid network (AAN) has become an emerging paradigm for studying FRs during the past decade. Current AAN models ignore the heterogeneity of nodes and treat amino acids in the AAN as the same. However, the properties of each amino acid node are of fundamental importance. We here proposed a node-weighted AAN strategy termed the node-weighted amino acid contact energy network (NACEN) to characterize and predict three types of FRs, namely, hot spots, catalytic residues, and allosteric residues. We first constructed NACENs with their nodes weighted based on structural, sequence, physicochemical, and dynamical properties of the amino acids and then characterized the FRs with the NACEN parameters. We finally built machine learning predictors to identify each type of FR. The results revealed that residues characterized with NACEN parameters are more distinguishable between FRs and non-FRs than those with unweighted network ones. With few features for classification, NACEN yields comparable performance for FR identification and provides residue level prediction for allosteric regulation. The proposed strategy can be easily implemented to other functional residue identification. An R package is also provided for NACEN construction and analysis at http://sysbio.suda.edu.cn/NACEN/index.html .