Potential Theory for Directed Networks

TL;DR

This paper introduces potential theory as a new principle for understanding the local structure of directed networks, supported by experiments showing its effectiveness in link prediction tasks.

Contribution

It proposes a novel potential theory mechanism for directed network organization and develops a link prediction algorithm based on this hypothesis.

Findings

Bi-fan structure is the most favored local pattern in directed networks.

The proposed predictor outperforms existing methods in link prediction accuracy.

Extensive experiments validate the potential theory hypothesis across diverse networks.

Abstract

Uncovering factors underlying the network formation is a long-standing challenge for data mining and network analysis. In particular, the microscopic organizing principles of directed networks are less understood than those of undirected networks. This article proposes a hypothesis named potential theory, which assumes that every directed link corresponds to a decrease of a unit potential and subgraphs with definable potential values for all nodes are preferred. Combining the potential theory with the clustering and homophily mechanisms, it is deduced that the Bi-fan structure consisting of 4 nodes and 4 directed links is the most favored local structure in directed networks. Our hypothesis receives strongly positive supports from extensive experiments on 15 directed networks drawn from disparate fields, as indicated by the most accurate and robust performance of Bi-fan predictor within the link prediction framework. In summary, our main contribution is twofold: (i) We propose a new mechanism for the local organization of directed networks; (ii) We design the corresponding link prediction algorithm, which can not only testify our hypothesis, but also find out direct applications in missing link prediction and friendship recommendation.