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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Emergent Optimal Frustration Density in Signed Relational Networks

Authors: Melegh, Janos Gabor;

Emergent Optimal Frustration Density in Signed Relational Networks

Abstract

We investigate how signed relational structure shapes emergent geometric organization in complex networks. Using signed small-world graphs with a tunable fraction of negative edges, we introduce a frustration-sensitive cancellation index that quantifies global incompatibility arising from opposing relational contributions. Across numerical experiments, global frustration exhibits a robust non-monotonic dependence on negative-edge density: frustration is maximized at an intermediate, sharply localized sign density rather than increasing monotonically. A refined scan yields an optimal frustration density q* ≈ 0.4946 ± 0.0044 (bootstrap std ≈ 0.0037 at N=200), robust to coarse-graining and stable under resampling. Repeating the analysis for N=150–300 shows no statistically significant finite-size drift within uncertainty; a constant model provides the most stable description over this range. These results indicate an emergent global frustration scale characteristic of a glassy crossover regime, distinct from a critical phase transition.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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