Spatio-temporal (ST) models are often used for analyzing ST phenomena. One such analysis technique is to detect patterns in the phenomenon to understand its evolution and model the behaviour of its entities over space-time. In this paper, we focus on using a dynamic graph-based representation for modeling ST phenomena, within which structural patterns, also modeled using dynamic graphs, can be detected. We illustrate the concept of pattern using two applications - road traffic and invasive team sports. For both these applications, we present the graph model as well as the corresponding patterns. Then we formalize the problem of pattern detection as that of subgraph isomorphism for dynamic graphs. Finally, we present the results of our algorithm to solve this problem. The initial results described in this paper, obtained using random graphs, present a baseline for the future tests of the algorithm.