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Assessing imbalance in signed brain networks

Marzio Di Vece1,2,*, Emanuele Agrimi2,3,4, Samuele Tatullo2, Tommaso Gili2, Miguel Ibáñez-Berganza2,5, and Tiziano Squartini1,2,5

  • *Contact author: marzio.divece@sns.it
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Phys. Rev. Research 8, 033301 – Published 11 September, 2026

DOI: https://doi.org/10.1103/p6qp-2s9f

Abstract

Many complex systems—be they financial, natural, or social—are composed of units—such as stocks, neurons, or agents—whose joint activity can be represented as a multivariate time series. An issue of both practical and theoretical importance concerns the possibility of inferring the presence of a static relationship between any two units solely from their dynamic behavior. The present contribution aims at tackling such an issue within the framework of traditional hypothesis testing: Briefly speaking, our suggestion is that of linking any two units if behaving in a sufficiently similar way. To achieve such a goal, we project a multivariate time series onto a signed graph by (1) comparing the empirical properties of the former with those expected under a suitable benchmark and (2) linking any two units with a positive (negative) edge in case the corresponding series shares a significantly large number of concordant (discordant) values. To define our benchmarks, we adopt an information-theoretic approach that is rooted into the constrained maximization of Shannon entropy, a procedure inducing an ensemble of multivariate time series that preserves some of the empirical properties on average, while randomizing everything else. We showcase the possible applications of our method by addressing one of the most timely issues in the domain of neurosciences, i.e., that of determining whether brain networks are frustrated or not, and, if so, to what extent. As our results suggest, this is indeed the case, with the major contribution to the underlying negative subgraph coming from the subcortical regions (and, to a lesser extent, from the limbic ones). At the mesoscopic level, the minimization of the Bayesian information criterion, instantiated with the signed stochastic block model, reveals that brain regions gather into modules aligning with the statistical variant of the relaxed balance theory.

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Phys. Rev. Research 8, 033301– Published 11 September, 2026
  • Received 1 October 2025
  • Accepted 15 June 2026
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