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Published on: December 7, 2021
Edge direction and the structure of networks
Jacob G Foster1, David V Foster, Peter Grassberger
1Complexity Science Group, Department of Physics and Astronomy, University of Calgary, 2500 University Drive NW, Calgary, AB, Canada. jgfoster@uchicago.edu
Summary
Edge direction significantly impacts network assortativity, a measure of node connection tendencies. New directed assortativity measures reveal complex patterns, challenging previous classifications of directed networks.
Area of Science:
- Network science
- Graph theory
- Complex systems analysis
Background:
- Directed networks, essential for asymmetric interactions, are prevalent in systems like food webs and the World Wide Web.
- Assortativity, the tendency for nodes with similar edge counts to connect, influences network properties but has been overlooked in directed networks.
Purpose of the Study:
- To investigate the impact of edge direction on network assortativity.
- To develop and apply novel measures for directed assortativity.
Main Methods:
- Defined four new measures for directed assortativity.
- Assessed statistical significance through comparison with randomized networks.
- Applied measures to online/social networks, food webs, and word-adjacency networks.
Main Results:
- Revealed common and distinct assortativity patterns across different network classes.
- Differentiated networks previously grouped together based on directed assortativity.
- Highlighted limitations in existing theoretical models for directed networks.
Conclusions:
- Edge direction profoundly influences network assortativity.
- Directed networks exhibit a mixture of assortative and disassortative behaviors, specific to their class.
- The findings challenge the simple classification of directed networks as purely assortative or disassortative.
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