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

TL;DR

This paper introduces a novel disparity-in-differences filter to extract hierarchical backbones from weighted directed networks, capturing asymmetric dependencies and hierarchical relations more effectively than existing methods.

Contribution

The paper proposes an extended disparity filter that incorporates node dependency to better identify hierarchical structures in complex networks.

Findings

Better captures hierarchical relations in diverse networks

Aligns with known hierarchical categories like journal quality and hub size

Outperforms traditional disparity filter in extracting meaningful backbones

Abstract

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.