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Emerging shared mobility systems are gaining popularity due to their significant economic and environmental benefits. In this paper, we present a network-based approach for predicting travel demand between stations (e.g., whether two stations have sufficient trips to form a strong connection) in shared mobility systems to support system design decisions. In particular, we answer the research question of whether local network information (e.g., the network neighboring station's features of a station and its surrounding points of interest (POI), such as banks, schools, etc.) would influence the formation of a strong connection or not. If so, to what extent do such factors play a role? To answer this question, we propose using graph neural networks (GNNs), in which the concept of network embedding can capture and quantify the effect of local network structures. We compare the results with a regular artificial neural network (ANN) model that is agnostic to neighborhood information. This study is demonstrated using a real-world bike sharing system, the Divvy Bike in Chicago. We observe that the GNN prediction gains up to 8% higher performance than the ANN model. Our findings show that local network information is vital in the structure of a sharing mobility network, and the results generalize even when the network structure and density change significantly. With the GNN model, we show how it supports two crucial design decisions in bike sharing systems, i.e., where new stations should be added and how much capacity a station should have. [ABSTRACT FROM AUTHOR]