Inferring resting-state functional connectivity (FC) from anatomical brain wiring, known as structural connectivity (SC), is of enormous significance in neuroscience for understanding biological neuronal networks and treating mental diseases. Both SC and FC are networks where the nodes are brain regions, and in SC, the edges are the physical fiber nerves among the nodes, while in FC, the edges are the nodes' coactivation relations. Despite the importance of SC and FC, until very recently, the rapidly growing research body on this topic has generally focused on either linear models or computational models that rely heavily on heuristics and simple assumptions regarding the mapping between FC and SC. However, the relationship between FC and SC is actually highly nonlinear and complex and contains considerable randomness; additional factors, such as the subject's age and health, can also significantly impact the SC-FC relationship and hence cannot be ignored. To address these challenges, here, we develop a novel SC-to-FC generative adversarial network (SF-GAN) framework for mapping SC to FC, along with additional metafeatures based on a newly proposed graph neural network-based generative model that is capable of learning the stochasticity. Specifically, a new graph-based conditional generative adversarial nets model is proposed, where edge convolution layers are leveraged to encode the graph patterns in the SC in the form of a graph representation. New edge deconvolution layers are then utilized to decode the representation back to FC. Additional metafeatures of subjects' profile information are integrated into the graph representation with newly designed sparse-regularized layers that can automatically select features that impact FC. Finally, we have also proposed new post hoc explainer of our SF-GAN, which can identify which subgraphs in SC strongly influence which subgraphs in FC by a new multilevel edge-correlation-guided graph clustering problem. The results of experiments conducted to test the new model confirm that it significantly outperforms existing state-of-the-art methods, with additional interpretability for identifying important metafeatures and subgraphs.