Predicting unknown directed links of conserved networks from flow data

Abstract Link prediction between nodes is an important problem in the study of complex networks. In this work, we investigate determining directed links in conserved flow networks from data. A novel approach to predict the unknown links of an underlying conserved network, and the directions of flows associated with them are proposed. The directed link prediction is achieved by finding the missing values in the incidence matrix of the network by combining singular value decomposition, principal component analysis and tools from graph theory using steady-state flow data. In contrast to traditional integer optimization-based approaches, the proposed approach accomplishes the task of directed link prediction in cubic time. The methodology is corroborated via synthetic studies for flow data generated from networks based on Erdős–Rényi, Watts–Strogatz and Barabási–Albert network models at different signal-to-noise ratios. It is empirically shown that all unknown directed links can be correctly predicted with large enough noisy data, in an asymptotic sense, to correctly estimate the missing values in the incidence matrix.