PageRank centrality and algorithms for weighted, directed networks

PageRank (PR) is a fundamental tool for assessing the relative importance of the nodes in a network. In this paper, we propose a measure, weighted PageRank (WPR), extended from the classical PR for weighted, directed networks with possible non-uniform node-specific information that is dependent or independent of network structure. A tuning parameter leveraging node degree and strength is introduced. An efficient algorithm based on R program has been developed for computing WPR in large-scale networks. We have tested the proposed WPR on widely used simulated network models, and found it outperformed the classical PR. Additionally, we apply the proposed WPR to the real network data generated from World Input–Output Tables as an example, and have seen the results that are consistent with the global economic trends, which renders it a preferred measure in the analysis.