Triangle redundancy as a structural determinant of neural circuit robustness: a comparative Topostability analysis of basal ganglia and hippocampal architecture

Understanding why neural circuits differ in their structural robustness requires frameworks that operate independently of dynamical parameters. Weapply Topostability, a parameter-free topological method based on edge triangle counts, to characterise structural redundancy across canonical modelsof the basal ganglia (BG) and hippocampal circuits. For each edge, thetriangle count tri(e) determines whether it is structurally non-redundant (always fragile), minimally redundant (fragile), or redundant (stable), yieldinga network-level Fragility Index (FI).Across synthetic graphs of varying sizes and densities, we demonstratethat the number of structurally independent triangles is a monotonic determinant of FI, providing a general theoretical basis for comparing circuitarchitectures. Applied to biological circuits constructed from primary neuroanatomical literature, the canonical BG circuit exhibits FI=65 with a single structurally independent triangle (GPe–STN–GPi), while the hippocampal trisynaptic circuit exhibits FI=35 with three structurally independenttriangles, all formed by high-confidence anatomical connections.Degree-preserving randomisation (n = 408 and n = 683 rewirings, respectively) confirms that these values are not explained by degree constraintsalone: the BG topology yields higher fragility than 86% of degree-matchedrandom graphs, while the hippocampal topology yields lower fragility than91% of degree-matched random graphs. Both circuits occupy two oppositeregions of the topological space compatible with their degree constraints. Additional analyses of cerebellar and cortical microcircuit models are reportedas exploratory findings, conditional on anatomically uncertain edges.These results constitute a serious structural hypothesis: neural circuitswith distinct functional roles differ in their degree of triangle redundancy inways that are not explained by size, density, or degree distribution alone.Keywords: triangle redundancy, structural fragility, basal ganglia,hippocampus, network neuroscience, Topostability, topological robustness,degree-preserving randomisation, graph theory, neural circuits