The paper presents a solution to the problem of universal representation of graphs exemplifying communication network topologies with the help of neural networks. The proposed approach is based on message-passing neural networks (MPNN). The approach enables us to represent topologies and operational aspects of networks. The usefulness of the solution is illustrated with a case study of delay prediction in queuing networks. This shows that performance evaluation can be provided without having to apply complex modeling. In consequence, the proposed solution makes it possible to effectively apply methods elaborated in the field of machine learning in communications.