Decoupled Axes of Connectome Maturation: Cycle Climate Invariance during Hub Crystallization

Developing nervous systems face a fundamental stabilityplasticity dilemma: how canneural circuits undergo massive synaptic remodeling while maintaining functional integrity? Using the complete developmental connectome of Caenorhabditis elegans, we identify two decoupled topological axes that resolve this tension. We introduce Cycle Homogeneity (CH), measuring the ratio of 4-cycles to triangles normalized against degree-preserving null models, and Coupling Homogeneity (KH), quantifying the Spearman correlation between node degree and clustering coecient. Analyzing eight developmental stages from birth to adulthood [Witvliet et al., 2021], we nd that CH shows no signicant developmental trend at 0.768±0.015 (p= 0.45, n= 8), while KH drifts from −0.003 to −0.522 (Spearman ρ=−0.93, R2 = 0.85). The two axes are empirically decoupled (ρ(CH,KH) = 0.31, p= 0.46). The apparent increase in chordality during development is largely accounted for by KH drift (partial correlation p= 0.20 after controlling for KH). We interpret KH drift as hub crystallization the progressive de-triangulation of high-degree neurons as they specialize into integration hubswhile CH stationarity reects invariant spatial embedding constraints of the nerve ring. This two-axis framework separates what changes (hub architecture) from what is conserved (cycle climate), providing a general template for understanding topological dynamics in developing neural systems.