Dynamically changing graphs are a powerful abstraction used to represent temporal relationships and connections occurring between data entities in various real-world organizations, such as social and telecommunication networks. The increasing volume, variety and velocity of graph-structured data in many application domains have led to a development of large-scale graph processing systems. However, current state-of-the-art graph processing systems do not provide efficient support for streaming graph scenarios. In this report, we describe and discuss stream graph processing, which narrows the problem of traditional graph processing by focusing on near real-time analysis of dynamic graph data constructed and maintained from stream sources, as opposed to processing of historical graph datasets loaded from a disk storage. We provide an outline of challenges in stream graph processing and present our preliminary approach to designing a stream graph processing system done as a part of early PhD work.