Disparity-in-Differences: Extracting Hierarchical Backbones of Weighted Directed Networks

Networks are useful representations for complex systems. Especially, heterogeneous and asymmetrical relations commonly found in complex systems can be converted to weighted directed edges between nodes. The disparity filter (Serrano et al., 2009) has successfully extracted backbones, sets of important edges, from empirical networks but is not designed to incorporate node-node dependency that may encode hierarchical relations. This paper proposes an extended disparity filter named "disparity-in-differences" that assigns a synthetic relation between two nodes if one depends relatively more on the other where the extent of asymmetric dependence is measured by the disparity between a normalized edge weight difference and an expected edge weight difference. For evaluation, the proposed method is applied to a journal citation network, a U.S. airport network, the Enron email network, and a world trade network. Compared to the disparity filter, the proposed approach better captures hierarchical relations that align well with journal quality ratings, airport hub categories by size, levels of management, and a core-periphery structure of countries, respectively.