Potential Theory for Directed Networks

Details Potential Theory for Directed Networks Potential Theory for Directed Networks

2012-02-13

arxiv.org/abs/1202.2709v1

Physics

Data Analysis, Statistics and Probability

9 pages, 5 figures

Scientific paper

Uncovering mechanisms 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 on all nodes are preferred. Combining the potential theory with the clustering and homophily mechanisms, we deduce that the Bi-fan consisting of 4 nodes and 4 directed links is the most favoured local structure in directed networks. Our hypothesis get 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 contributions are twofold: (i) We propose a new mechanism for the organization of directed networks; (ii) We design the corresponding link prediction algorithm, which can not only testify our hypothesis, but also find direct applications in missing link prediction and friendship recommendation.

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