Researchers are solving the challenges of spatial-temporal prediction by combining Federated Learning (FL) and graph models with respect to the constrain of privacy and security. In order to make better use of the power of graph model, some researchs also combine split learning(SL). However, there are still several issues left unattended: 1) Clients might not be able to access the server during inference phase; 2) The graph of clients designed manually in the server model may not reveal the proper relationship between clients. This paper proposes a new GNN-oriented split federated learning method, named node {\bfseries M}asking and {\bfseries M}ulti-granularity {\bfseries M}essage passing-based Federated Graph Model (M$^3$FGM) for the above issues. For the first issue, the server model of M$^3$FGM employs a MaskNode layer to simulate the case of clients being offline. We also redesign the decoder of the client model using a dual-sub-decoders structure so that each client model can use its local data to predict independently when offline. As for the second issue, a new GNN layer named Multi-Granularity Message Passing (MGMP) layer enables each client node to perceive global and local information. We conducted extensive experiments in two different scenarios on two real traffic datasets. Results show that M$^3$FGM outperforms the baselines and variant models, achieves the best results in both datasets and scenarios.

Vast amount of data generated from networks of sensors, wearables, and the Internet of Things (IoT) devices underscores the need for advanced modeling techniques that leverage the spatio-temporal structure of decentralized data due to the need for edge computation and licensing (data access) issues. While federated learning (FL) has emerged as a framework for model training without requiring direct data sharing and exchange, effectively modeling the complex spatio-temporal dependencies to improve forecasting capabilities still remains an open problem. On the other hand, state-of-the-art spatio-temporal forecasting models assume unfettered access to the data, neglecting constraints on data sharing. To bridge this gap, we propose a federated spatio-temporal model -- Cross-Node Federated Graph Neural Network (CNFGNN) -- which explicitly encodes the underlying graph structure using graph neural network (GNN)-based architecture under the constraint of cross-node federated learning, which requires that data in a network of nodes is generated locally on each node and remains decentralized. CNFGNN operates by disentangling the temporal dynamics modeling on devices and spatial dynamics on the server, utilizing alternating optimization to reduce the communication cost, facilitating computations on the edge devices. Experiments on the traffic flow forecasting task show that CNFGNN achieves the best forecasting performance in both transductive and inductive learning settings with no extra computation cost on edge devices, while incurring modest communication cost.