Comparing Temporal Graphs Using Dynamic Time Warping

TL;DR

This paper introduces a novel flexible distance measure, dynamic temporal graph warping (dtgw), for comparing temporal graphs, demonstrating its effectiveness and computational challenges through experiments on real-world data.

Contribution

The paper proposes the dtgw distance for temporal graphs, analyzes its computational complexity, and develops a heuristic for practical comparison.

Findings

The dtgw distance performs well in network de-anonymization tasks.

Computing dtgw is NP-hard in general but has polynomial-time solvable cases.

The heuristic approach is efficient and effective on real data.

Abstract

Within many real-world networks the links between pairs of nodes change over time. Thus, there has been a recent boom in studying temporal graphs. Recognizing patterns in temporal graphs requires a proximity 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 dissimilarity 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 dtgw-distance performs favorably in de-anonymizing networks compared to other approaches.