Quantum cryptography provides a feasible approach to achieving information-theoretic security in point-to-point communication. In contrast to point-to-point protocols, end-to-end secure quantum communication is particularly promising for large-scale quantum networks. Here, we propose a scheme for end-to-end secure communication with private message authentication. For practical purposes, we demonstrate the scheme in a quantum communication network with optical fibers or free-space links that integrate secure repeaters. Furthermore, we present a route proposal model for routing private messages in a quantum network based on the scheme. As messages are routed through a network, malicious nodes may tamper with the messages passing through them with some probability. Based on authentication results, we use machine learning methods to detect malicious nodes, including supervised and unsupervised algorithms. The simulation results in specific networks show that our methods can effectively detect malicious nodes under different tamper probabilities.