We introduce the controllable graph generation problem, formulated as controlling graph attributes during the generative process to produce desired graphs with understandable structures. Using a transparent and straightforward Markov model to guide this generative process, practitioners can shape and understand the generated graphs. We propose ${\rm S{\small HADOW}C{\small AST}}$, a generative model capable of controlling graph generation while retaining the original graph's intrinsic properties. The proposed model is based on a conditional generative adversarial network. Given an observed graph and some user-specified Markov model parameters, ${\rm S{\small HADOW}C{\small AST}}$ controls the conditions to generate desired graphs. Comprehensive experiments on three real-world network datasets demonstrate our model's competitive performance in the graph generation task. Furthermore, we show its effective controllability by directing ${\rm S{\small HADOW}C{\small AST}}$ to generate hypothetical scenarios with different graph structures.