Comparing Temporal Graphs Using Dynamic Time Warping

Vincent Froese, Brijnesh J. Jain, Rolf Niedermeier, Malte Renken

Abstract: The links between vertices within many real-world networks change over time. Correspondingly, there has been a recent boom in studying temporal graphs. Proximity-based pattern recognition in temporal graphs requires a (dis)similarity measure to compare different temporal graphs. To this end, we propose to employ dynamic time warping on temporal graphs. We define the dynamic temporal graph warping distance (dtgw) to determine the (dis)similarity of two temporal graphs. Our novel measure is flexible and can be applied in various application domains. We show that computing the dtgw-distance is a challenging (in general NP-hard) optimization problem and we identify some polynomial-time solvable special cases. Moreover, we develop an efficient heuristic which performs well in empirical studies. In experiments on real-word data we show that our dtgw-distance performs favorably in de-anonymizing networks compared to other approaches.