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Bipartite structural evaluation: Extended network generation model and corrected randomization techniques

Harry de los Ríos1, María J. Palazzi1, Aniello Lampo2, Albert Solé-Ribalta1, and Javier Borge-Holthoefer1,*

  • *Contact author: jborgeh@uoc.edu
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Phys. Rev. Research 8, 013036 – Published 14 January, 2026

DOI: https://doi.org/10.1103/7t51-c6tx

Abstract

Understanding the structural organization of bipartite networks is essential for characterizing the architecture and dynamics of complex systems, from ecological communities to technological and social interactions. Such networks often exhibit recurring patterns—nestedness, modularity, in-block nestedness—that shape system stability, diversity, and function. Yet, despite extensive research, assessing the statistical significance of these patterns remains problematic, as existing null models may introduce systematic biases that can lead to contradictory interpretations. Here, we develop a generative framework that analytically constructs synthetic bipartite networks spanning the most common structural regimes and use it to perform a comprehensive evaluation of state-of-the-art null models. Across large synthetic and empirical ensembles, we show how commonly used null models inconsistently estimate the significance of nested, modular, and compound architectures, depending on how degree constraints are imposed. Building on these insights, we introduce a corrected probabilistic model that reconciles, to some extent, these inconsistencies, providing a more balanced basis for significance testing. Our work thus establishes a unified theoretical and computational framework for generating, analyzing, and interpreting structure in bipartite networks, offering conceptual and methodological guidance for future research in ecology and beyond.

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Phys. Rev. Research 8, 013036– Published 14 January, 2026
  • Received 11 April 2025
  • Accepted 24 December 2025
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