We present a physically inspired model and an efficient algorithm to infer hierarchical rankings of nodes in directed networks. It assigns real-valued ranks to nodes rather than simply ordinal ranks, and it formalizes the assumption that interactions are more likely to occur between individuals with similar ranks. It provides a natural statistical significance test for the inferred hierarchy, and it can be used to perform inference tasks such as predicting the existence or direction of edges. The ranking is obtained by solving a linear system of equations, which is sparse if the network is; thus, the resulting algorithm is extremely efficient and scalable. We illustrate these findings by analyzing real and synthetic data, including data sets from animal behavior, faculty hiring, social support networks, and sports tournaments. We show that our method often outperforms a variety of others, in both speed and accuracy, in recovering the underlying ranks and predicting edge directions.

中文翻译：

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在网络中进行有效排名的物理模型。

我们提出了一种物理启发模型和一种有效的算法来推断有向网络中节点的分层排名。它给节点分配实值秩，而不是简单地按序排列，并正式化了这样的假设：交互作用更可能发生在具有相似秩的个体之间。它为推断的层次结构提供了自然的统计显着性检验，并且可用于执行推断任务，例如预测边的存在或方向。通过求解线性方程组来获得排名，如果网络是稀疏的，则该稀疏。因此，所得算法非常有效且可扩展。我们通过分析实际和综合数据来说明这些发现，这些数据包括来自动物行为，教职员工，社会支持网络和体育比赛的数据集。