Recursive Structure as a Distinct Dimension of Network Dynamics: A Cycle-Based Metric Reveals Limitations of Integration and Correlation-Based Inference

Recursive Structure as a Distinct Dimension of Network Dynamics: A Cycle-Based Metric Reveals Limitations of Integration and Correlation-Based Inference | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Recursive Structure as a Distinct Dimension of Network Dynamics: A Cycle-Based Metric Reveals Limitations of Integration and Correlation-Based Inference Dewan Sajid Islam This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9449067/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Quantifying the relationship between network structure and emergent dynamics remains a central challenge in neuroscience and complex systems theory. Existing approaches predominantly emphasize global integration, as formalized in frameworks such as Integrated Information Theory (IIT), or rely on statistical measures derived from observed activity, such as correlation-based connectivity. However, these approaches do not explicitly capture recursive structure, defined as the presence of closed causal pathways enabling feedback. In this study, we introduce a cycle-based metric, Recursive Integration Depth (RIDv4), designed to quantify recursive structure in networked dynamical systems. Using simulated networks across multiple connectivity regimes, we demonstrate that RIDv4 distinguishes structured feedback networks from both weakly connected and randomly dense networks, even when integration is high. Comparisons with baseline cycle-counting and entropy-based metrics show that these approaches fail to reliably capture recursive organization. Furthermore, when applying RIDv4 to connectivity matrices inferred from time-series data, we observe a reversal effect: systems with true underlying feedback structure exhibit lower measured recursion than random systems. This indicates that correlation-based inference does not fully preserve recursive structure and may obscure underlying feedback dynamics. These findings suggest that recursive structure constitutes a meaningful structural property not captured by standard integration or statistical approaches, and that its detection depends critically on how network representations are constructed. Biological sciences/Computational biology and bioinformatics Physical sciences/Mathematics and computing Biological sciences/Neuroscience Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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