Network functions virtualization (NFV) continues to gain attention as a paradigm shift in the way telecommunications services are deployed and managed. By separating network function from traditional middleboxes, NFV is expected to lead to reduced capital expenditure and operating expenditure, and to more agile services. However, one of the main challenges to achieving these objectives is how physical resources can be efficiently, autonomously, and dynamically allocated to virtualized network function (VNF) whose resource requirements ebb and flow. In this paper, we propose a graph neural network-based algorithm which exploits VNF forwarding graph topology information to predict future resource requirements for each VNF component (VNFC). The topology information of each VNFC is derived from combining its past resource utilization as well as the modeled effect on the same from VNFCs in its neighborhood. Our proposal has been evaluated using a deployment of a virtualized IP multimedia subsystem, and real VoIP traffic traces, with results showing an average prediction accuracy of 90%, compared to 85% obtained while using traditional feed-forward neural networks. Moreover, compared to a scenario where resources are allocated manually and/or statically, our technique reduces the average number of dropped calls by at least 27% and improves call setup latency by over 29%.