Curvature on Graphs with Negative Edge Weights
Daniel Grange1, Yifan Sun1, Corey Weistuch2
1Department of Computer Science, Stony Brook University, Stony Brook, NY 11794, USA.
IEEE Transactions on Network Science and Engineering
|May 1, 2026
Summary
This study introduces graph frustration and new Ollivier-Ricci-inspired fragility indices for analyzing signed networks. These indices effectively identify critical pathways in gene regulatory and social networks, outperforming existing measures.
Area of Science:
- Network Science
- Graph Theory
- Mathematical Modeling
Background:
- Discrete curvature measures offer insights into network fragility.
- Ollivier-Ricci (OR) curvature extends geometric concepts to graphs.
- Existing methods do not capture antagonistic relationships in networks.
Purpose of the Study:
- Introduce "balanced" graphs and "graph frustration" to model signed network interactions.
- Develop modified Ollivier-Ricci-inspired fragility indices.
- Evaluate the utility of these new indices in identifying critical pathways.
Main Methods:
- Defined balanced graphs and graph frustration based on signed edge weights (promotion/inhibition).
- Developed modified Ollivier-Ricci-inspired fragility indices.
- Applied indices to gene regulatory and social networks.
Main Results:
- The new fragility indices effectively identify critical edges in unbalanced graphs.
- These indices outperform commonly used measures in quantifying network criticality.
- Demonstrated utility in gene regulatory and social network analysis.
Conclusions:
- Graph frustration and modified OR-inspired indices provide novel tools for analyzing signed networks.
- These methods enhance the identification of critical nodes and pathways.
- The approach offers improved understanding of network functionality and disruption.
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