A physical model for efficient ranking in networks

TL;DR

This paper introduces a physically-inspired, scalable algorithm for inferring hierarchical node rankings in directed networks, outperforming existing methods in speed and accuracy across various real-world datasets.

Contribution

It proposes a novel method that assigns real-valued ranks, formalizes interaction likelihood based on rank similarity, and provides a statistical significance test for hierarchy inference.

Findings

Method outperforms others in speed and accuracy

Effective in diverse datasets including animal behavior and social networks

Provides a natural statistical significance test for hierarchy

Abstract

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 datasets 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.