Core-periphery structure in directed networks.

Area of Science:

• Network Science
• Graph Theory
• Data Mining

Background:

• Empirical networks commonly display meso-scale structures like communities and core-periphery organization.
• Core-periphery structures feature a dense core and a periphery connected to the core but not internally.
• Existing research predominantly focuses on undirected networks, leaving directed network structures less explored.

Purpose of the Study:

• To generalize the concept of core-periphery structure to directed networks.
• To develop and validate methods for detecting and assessing this structure in empirical directed networks.
• To provide a framework for analyzing directed network organization that accounts for edge directionality.

Main Methods:

• Proposed a generalization of core-periphery structure for directed networks, defining edge-direction dependent core and periphery sets.
• Developed two measures for assessing the statistical significance and quality of the identified structure.
• Adapted three existing methods to detect core-periphery structures in directed networks, evaluating trade-offs in computational complexity and accuracy.

Main Results:

• The proposed methods were tested on benchmark networks, demonstrating comparable or superior performance to existing approaches.
• A likelihood-based approach emerged as the most accurate method for detecting directed core-periphery structures.
• Application to faculty hiring, world trade, and political blog networks revealed novel insights into their organizational patterns.

Conclusions:

• The generalized core-periphery structure effectively captures directed network organization.
• The developed methods provide reliable tools for analyzing complex directed networks.
• This framework enhances understanding of meso-scale structures in diverse empirical network datasets.