The dynamic nature of real-world networks, such as social networks and communication networks, has increased the focus towards real-time dynamic graph analysis. Observations made based on real-time analysis of dynamic graphs reflect the latest properties of the graph and have the most value in real-time analysis. Computing graph properties of large-scale, fast-evolving graphs in real-time is challenging due, not only to the high computational and memory cost, but also to the understanding of the result with respect to the data from which it was derived. This paper proposes a multi-stage hierarchical window model that can aid in rigorous understanding of complicated real-time results and we apply it to generate graphs based on real-time updates along with periodic computations on graph snapshots for processing dynamic graphs. Moreover, the paper discusses the utilization of parallel window computation. The paper evaluates the hierarchical model through analyzing graphs formed by cooccurring hashtags in a Twitter data-stream.