We present a physics-inspired method for inferring dynamic rankings in directed temporal networks - networks in which each directed and timestamped edge reflects the outcome and timing of a pairwise interaction. The inferred ranking of each node is real-valued and varies in time as each new edge, encoding an outcome like a win or loss, raises or lowers the node's estimated strength or prestige, as is often observed in real scenarios including sequences of games, tournaments, or interactions in animal hierarchies. Our method works by solving a linear system of equations and requires only one parameter to be tuned. As a result, the corresponding algorithm is scalable and efficient. We test our method by evaluating its ability to predict interactions (edges' existence) and their outcomes (edges' directions) in a variety of applications, including both synthetic and real data. Our analysis shows that in many cases our method's performance is better than existing methods for predicting dynamic rankings and interaction outcomes.

翻译：我们提出了一种受物理学启发的方法，用于推断有向时序网络——即每条带时间戳的有向边反映成对交互结果与时间的网络——中的动态排序。每个节点的推断排序值为实数，并随时间动态变化：每当出现一条编码胜负等结果的新边时，节点估计强度或声望值会相应升降。这一现象常见于实际场景，包括比赛序列、锦标赛或动物社会等级中的交互。该方法通过求解线性方程组实现，且仅需调节一个参数。因此，对应算法具有良好的可扩展性和高效性。我们通过预测交互（边的存在性）及其结果（边的方向性）的能力来评估该方法，测试涉及合成数据与真实数据等多种应用场景。分析表明，在多种情况下，该方法在动态排序和交互结果预测方面的性能均优于现有方法。