Researchers, policy makers, and engineers need to make sense of data from spreading processes as diverse as rumor spreading in social networks, viral infections, and water contamination. Classical questions include predicting infection behavior in a given network or deducing the network structure from infection data. Most of the research on network infections studies static graphs, that is, the connections in the network are assumed to not change. More recently, temporal graphs, in which connections change over time, have been used to more accurately represent real-world infections, which rarely occur in unchanging networks. We propose a model for temporal graph discovery that is consistent with previous work on static graphs and embraces the greater expressiveness of temporal graphs. For this model, we give algorithms and lower bounds which are often tight. We analyze different variations of the problem, which make our results widely applicable and it also clarifies which aspects of temporal infections make graph discovery easier or harder. We round off our analysis with an experimental evaluation of our algorithm on real-world interaction data from the Stanford Network Analysis Project and on temporal Erd\H{o}s-Renyi graphs. On Erd\H{o}s-Renyi graphs, we uncover a threshold behavior, which can be explained by a novel connectivity parameter that we introduce during our theoretical analysis.

翻译：研究人员、政策制定者和工程师需要理解各种传播过程产生的数据，这些过程涵盖社交网络中的谣言传播、病毒感染以及水污染等。经典问题包括预测给定网络中的感染行为，或从感染数据推断网络结构。现有关于网络感染的研究大多针对静态图，即假设网络中的连接关系保持不变。近年来，时态图（其中连接关系随时间变化）被用于更准确地表征现实世界的感染过程，因为实际感染很少发生在固定不变的网络中。我们提出了一种时态图发现模型，该模型既与静态图研究的既有成果保持连贯，又充分体现了时态图更强的表达能力。针对该模型，我们给出了算法及其下界，这些下界通常是最优的。我们分析了该问题的多种变体，这使得我们的研究成果具有广泛适用性，同时也明确了时态感染的哪些特性会使图发现任务变得更容易或更困难。最后，我们通过实验评估完善了分析：使用斯坦福网络分析项目的真实世界交互数据与时态Erd\H{o}s-Renyi图对算法进行测试。在Erd\H{o}s-Renyi图上，我们发现了一种阈值现象，该现象可通过理论分析中引入的新颖连通性参数得到解释。