Graph embedding has been intensively studied recently, due to the advance of various neural network models. Theoretical analyses and empirical studies have pushed forward the translation of discrete graph structures into distributed representation vectors, but seldom considered the reverse direction, i.e., generation of graphs from given related context spaces. Particularly, since graphs often become more meaningful when associated with semantic contexts (e.g., social networks of certain communities, gene networks of certain diseases), the ability to infer graph structures according to given semantic conditions could be of great value. While existing graph generative models only consider graph structures without semantic contexts, we formulate the novel problem of conditional structure generation, and propose a novel unified model of graph variational generative adversarial nets (CondGen) to handle the intrinsic challenges of flexible context-structure conditioning and permutation-invariant generation. Extensive experiments on two deliberately created benchmark datasets of real-world context-enriched networks demonstrate the supreme effectiveness and generalizability of CondGen.