Making analogies is an important way for people to explain and understand new concepts. Though making analogies is natural for human beings, it is not a trivial task for a dialogue agent. Making analogies requires the agent to establish a correspondence between concepts in two different domains. In this work, we explore a data-driven approach for making analogies automatically. Our proposed approach works with data represented as a flat graphical structure, which can either be designed manually or extracted from Internet data. For a given concept from the base domain, our analogy agent can automatically suggest a corresponding concept from the target domain, and a set of mappings be-tween the relationships each concept has as supporting evidence. We demonstrate the working of this algorithm by both reproducing a classical example of analogy inference and making analogies in new domains generated from DBPedia data.