Graph Topology Reframes the Coherence of Cell-State Manifold Inference under Heterogeneous Single-Cell Observations

Manifold-based single-cell omics analyses assume that high-dimensional observations can fall into a low-dimensional space encoding biological constraints. In practice, per-cell observation is highly heterogeneous: Shallowly and deeply observed cells coexist. In an empirical single-cell RNA sequencing dataset, shallowly observed cells cluster together to generate spurious hubs that can give rise to illusory loops in low-dimensional manifold skeletons in graph abstraction. Several imputation methods leave these artifacts largely intact, whereas graph abstraction restricted to homogeneously observed cells alone recovers tree-like structures locally representing constrained cell state transitions. Simulations further demonstrate that realistic heterogeneous observation can create spurious subclusters and false branching. Grounded by these observations, we propose topological stability descriptors of low-dimensional manifold skeletons to delineate a regime in which manifold-based inference is trustworthy despite realistic heterogeneous observations. Our findings underscore that the heterogeneity of observations is not merely noise but a source of systemic distortion in manifold-based inference that must be addressed.