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Graphs are universal representations of pairwise information in many domains, e.g.,social networks and molecule structures. The problem of deep graph generation which is handled by deep generative models has attracted great attentions in the most recent years. However, it is usually desirable to guide the graph generation process by conditioning on additional information such as data from the different modality, which is also coined as conditional graph generation (i.e., graph transformation). Conditional graph generation can be seen in many real-world applications such as Internet of Things (IoT) confinement and chemical reactant prediction. In addition, the existing graph generation works neglect the entanglement of the encoded latent factors, rendering the generation process non-robust and hardly explainable. Therefore, the general goal of this research is how to develop the graph deep generative models for conditional and interpretable graph generation. To solve the above problems, there are two main aims to be achieved: (1) The conditionalgraph generation aims to control the generation process on a specific input graph. One needs to not only learn the transformation mapping in the local information of a graph (i.e., neighborhood pattern of each node), but also in the global property of the whole graph (e.g., node degree distribution or graph density). It is also very important to deal with more general graph transformation problem for various graph types, such as the multiattributed graphs, the signed graphs and directed graphs. (2) The interpretation of the graph generation process is also imperative but unexplored. The complex formation process of graphs requires the model to have a sophisticated mechanism for inferring the latent factor that may cause an edge of a specific node and the global properties of the whole graph. This mechanism needs to be differentiable to support end-to-end training and be capable of conducting inductive learning to enable out-of-sample node processing in real-time for real-world deployment. To achieve the above goals, we first present a novel framework for conditional deepgraph topology generation with a graph-translation generative adversarial nets (GT-GAN). GT-GANs learn a conditional generative model, which is a graph translator that transforms an input graph to a target graph. For a more generalized problem, we propose a node-edge co-evolution framework for the multi-attributed graph transformation considering both the directed and sign graphs. Secondly, to interpret the generation process, we first propose a novel Variational Auto-encoder (VAE)-based graph generative model which can learn the disentangled latent representations as well as semantic factors for interpreting the generation process. In addition, to further precisely control the generation process, we propose a property controllable generative model for manipulating the generated graphs with desired properties. This research spans multiple disciplines and promises to make general contributions invarious domains such as deep learning, explainable AI, molecular modeling, and computational biology by putting forth a novel algorithm that can be applied to various real-world network transformation and generation problems, ranging from cyber network transformation to novel molecule structure generation.