Original title: Sectoral inter-dependencies drive the loss of structural balance in signed financial networks
Kartik Dahake, Abhijit Chakraborty · August 2026
In the stock market, asset prices can move together in harmony or in conflict. Researchers model these positive and negative connections as signed networks. During economic crises, the financial system loses structural balanceA property of a signed network in which triangles of relationships follow consistent sign patterns; when those patterns break, the network is imbalanced., but scientists did not know where this breakdown begins. To find out, the researchers analyzed long-term price data from the S&P 500 index. They measured network balance across different levels using polarizationA measure of how far the network is from balanced, based on the signs around small groups of nodes., a metric based on three-asset relationship patterns called triadic motifsSmall patterns of three nodes and the links among them; here they are the basic units used to measure balance.. They discovered that during times of systemic risk, this imbalance comes mainly from conflicts between different market sectors rather than within single sectors. Using randomization tests, they confirmed these patterns are real and not random noise. Finally, they found that low polarization during crises is driven by pressures from inflation uncertainty and supply chain disruptions. This shows how tensions between specific sectors spread across the entire market, creating large-scale instability.
Imagine a neighborhood potluck where every household has a standing feeling about every other household — warm or cold. Normally you expect a friend of a friend to also be a friend, and when that pattern breaks, the whole atmosphere feels tense. In this paper, the households are companies, warm or cold stands for whether their prices tend to move together or apart, and the tension is measured across the whole system. The surprise: during a crisis, the tension comes mostly from relationships between different neighborhoods, not from feuds inside one neighborhood.
For anyone watching markets, this changes where to look: the danger signal lives in how sectors interact, not in what happens inside a single sector. It links a measurable property of the network — its polarization — to concrete economic pressures like supply-chain disruptions and inflation uncertainty. That gives a quantitative way to see how localized sectoral conflicts become large-scale instability.
The abstract doesn't say how much variance the regression explains or list its coefficients, so the strength of the macroeconomic link is not quantified here. It also doesn't test whether the pattern generalizes beyond the S&P 500 or beyond crisis periods.
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Sectoral inter-dependencies drive the loss of structural balance in signed financial networks — Kartik Dahake, Abhijit Chakraborty
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.