We propose a graph neural network (GNN) architecture to optimize base station (BS) beamforming and reconfigurable intelligent surface (RIS) phase shifts in a multi-RIS assisted wireless network. We create a bipartite graph model to represent a network with multi-RIS, then construct the GNN architecture by exploiting channel information as node and edge features. We employ a message passing mechanism to enable information exchange between RIS nodes and user nodes and facilitate the inference of interference. Each node also maintains a representation vector which can be mapped to the BS beamforming or RIS phase shifts output. Message generation and update of the representation vector at each node are performed using two unsupervised neural networks, which are trained off-line and then used on all nodes of the same type. Simulation results demonstrate that the proposed GNN architecture provides strong scalability with network size, generalizes to different settings, and significantly outperforms conventional algorithms.