  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.
