Detecting dynamic patterns in dynamic graphs using subgraph isomorphism

Graphs have been used in different fields of research for performing structural analysis of various systems. In order to compare the structure of two systems, the correspondence between their graphs has to be verified. The problem of graph matching, especially subgraph isomorphism (SI), has been well studied in case of static graphs. However, many applications require incorporating temporal information, making the corresponding graphs dynamic. In this paper, we apply SI to detect dynamic patterns in dynamic graphs. We propose an algorithm for induced SI to detect all the matchings for a given pattern graph while considering snapshot-based representation of dynamic graphs and taking into account the chronological order of these snapshots. This is the novelty of the proposed approach since the existing state-of-the-art algorithms model dynamic graphs using an aggregated model with time-stamped edges. To the best of our knowledge, there does not exist another approach which considers snapshot-based representation of dynamic pattern and dynamic target graphs for this problem. We discussed the time complexity of our algorithm and tested its performance while comparing it with two existing algorithms using the real-world datasets. It was found that our algorithm is the second best overall in terms of the execution time. The results are promising given the fact that the choice of dynamic graph model affects the algorithmic design for solving the problem of SI. For the applications where aggregated model of dynamic graphs is not applicable and snapshot-based representation is indispensable, our algorithm can be directly applied as opposed to the existing ones.