With increasing data and technology, multiple types of data from the same set of nodes have been generated. Since each data modality contains a unique aspect of the underlying mechanisms, multiple datatypes are integrated. In addition to multiple datatypes, networks are important to store information representing associations between entities such as genes of a protein-protein interaction network and authors of a citation network. Recently, some advanced approaches to graph-structured data leverage node associations and features simultaneously, called Graph Neural Network (GNN), but they have limitations for integrative approaches. The overall aim of this dissertation is to integrate multiple data modalities on graph-structured data to infer some context-specific gene regulation and predict outcomes of interest. To this end, first, we introduce a computational tool named CRINET to infer genome-wide competing endogenous RNA (ceRNA) networks. By integrating multiple data properly, we had a better understanding of gene regulatory circuitry addressing important drawbacks pertaining to ceRNA regulation. We tested CRINET on breast cancer data and found that ceRNA interactions and groups were significantly enriched in the cancer-related genes and processes. CRINET-inferred ceRNA groups supported the studies claiming the relation between immunotherapy and cancer. Second, we present SUPREME, a node classification framework, by comprehensively analyzing multiple data and associations between nodes with graph convolutions on multiple networks. Our results on survival analysis suggested that SUPREME could demystify the characteristics of classes with proper utilization of multiple data and networks. Finally, we introduce an attention-aware fusion approach, called GRAF, which fuses multiple networks and utilizes attention mechanisms on graph-structured data. Utilization of learned node- and association-level attention with network fusion allowed us to prioritize the edges properly, leading to improvement in the prediction results. Given the findings of all three tools and their outperformance over state-of-the-art methods, the proposed dissertation shows the importance of integrating multiple types of data and the exploitation of multiple graph structured data.