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：我们提出一种受物理学启发的、用于推断有向时序网络中动态排序的方法——该类网络中的每条带时间戳的有向边均反映了一次成对交互的结果与发生时刻。每个节点的推断排序值为实数，并随时间变化：每条新边（编码了如胜负等结果）会提升或降低该节点的估计强度或声望，这常见于真实场景，包括一系列比赛、锦标赛或动物等级体系中的交互。我们的方法通过求解线性方程组实现，仅需调整一个参数。因此，相应算法具备可扩展性与高效性。我们通过评估该方法在多种应用（包括合成数据与真实数据）中预测交互（边的存在性）及其结果（边的方向）的能力来对其进行测试。分析表明，在多数情况下，本方法在预测动态排序与交互结果方面的性能优于现有方法。