The classification of networked data is an interesting and challenging problem. Most traditional relational classifiers that are based on the principle of homophily have an unsatisfactory classification performance in networks with heterophily. This is because these methods treat inhomogeneous networks homogeneously. A progression of a network-only Bayes-classifier-based second-order Markov assumption is proposed for heterophilous networks in this paper to address this problem. First, we estimate the class distribution of an unlabeled node according to the class distribution of its neighbors' neighbors. In this process, we perform this computation on the known and unknown neighbors separately. Second, we combine the two parts using multinomial naïve Bayesian classification. Meanwhile, we pair a relaxation labeling collective inference method (which imports simulated annealing) with this new method to update the class distributions at each iteration. Comparisons of the experimental results demonstrate that the proposed method performs better when the networks are heterophilous. INDEX TERMS Artificial intelligence, data mining, heterophilous networks, machine learning, networked data classification, relational classifier.