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

Developing nervous systems face a fundamental stability-plasticity dilemma: how can neural circuits undergo massive synaptic remodeling while maintaining functional integrity? Using the complete developmental connectome of Caenorhabditis elegans, we identify two orthogonal 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 coefficient. Analyzing eight developmental stages from birth to adulthood (Witvliet et al., 2021), we find that CH remains stationary at 0.768 ± 0.016 (p = 0.49 for trend), while KH exhibits monotonic drift from −0.003 to −0.524 (R² = 0.87). Cross-validation against an independent reconstruction (Brittin et al., 2021) confirms CH invariance (ΔCH = 0.003). The apparent increase in chordality during development is entirely explained as epiphenomenal to KH drift (partial correlation p = 0.23). We interpret KH drift as hub crystallization—the progressive de-triangulation of high-degree neurons as they specialize into integration hubs—while CH stationarity reflects 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.