Comparing Temporal Graphs Using Dynamic Time Warping

The links between pairs of nodes within many real-world networks change over time. Thus, there has been a recent boom in studying temporal graphs. Recognizing patterns in temporal graphs requires a similarity measure to compare different temporal graphs. To this end, we propose to study 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 identify some polynomial-time solvable special cases. Moreover, we develop a quadratic programming formulation and an efficient heuristic. In experiments on real-word data we show that the heuristic performs very well and that our approach performs favorably in de-anonymizing networks compared to other approaches.