Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at different time points. However, quantifying the similarity between temporal graphs as a whole is an open problem. Here, we use embeddings based on time-respecting random walks to introduce a new notion of distance between temporal graphs. This distance is well-defined for pairs of temporal graphs with different numbers of nodes and different time spans. We study the case of a matched pair of graphs, when a known relation exists between their nodes, and the case of unmatched graphs, when such a relation is unavailable and the graphs may be of different sizes. We use empirical and synthetic temporal network data to show that the distance we introduce discriminates graphs with different topological and temporal properties. We provide an efficient implementation of the distance computation suitable for large-scale temporal graphs.

翻译：时序图常用于表示众多自然与人工系统中实体间随时间演化的关系。现有大量技术通过比较不同时间点的图状态来探究时序图的演化规律。然而，如何量化时序图整体间的相似性仍是一个开放性问题。本文提出一种基于时间约束随机游走嵌入的新颖时序图距离度量方法。该距离度量适用于具有不同节点数量和时间跨度的时序图对。我们研究了两种情形：匹配图对（节点间存在已知对应关系）与非匹配图对（节点对应关系未知且图规模可能不同）。通过实证与合成时序网络数据，我们证明所提出的距离度量能够有效区分具有不同拓扑结构与时间特性的图。本文同时提供了适用于大规模时序图的高效距离计算实现方案。