A physical model for efficient ranking in networks
This work addresses the need for scalable and accurate ranking methods in various domains like social networks and sports, but it is incremental as it builds on existing ranking approaches with a new model.
The authors tackled the problem of inferring hierarchical rankings in directed networks by developing a physically-inspired model that assigns real-valued ranks and assumes interactions occur between similarly-ranked nodes, resulting in an efficient linear system algorithm that outperforms other methods in speed and accuracy for recovering ranks and predicting edge directions.
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.