Choose a task | A small workflow, with stopping points | Function catalog | Prepare and assign | Fit and inspect a hierarchy | Reuse and display | Matrix and identity conventions | Unordered dominance sets | Filtering, scaling and grouping answer different questions | Ties and random seeds | What a dCST hierarchy stores | Refinement choices | Landmarks are selected observations | The optional pipeline | Transfer to a frozen reference | Inspect a transfer decision and saved refinement settings | Embeddings and display labels | Resource planning | Finding help and migrating older code | Triple-supported pair-state graphs

Generate the observations | Distances and the path graph | Compare with surface geodesics | Inspect supporting edges in three dimensions | Chord lengths before and after scaling | Paraboloid reference-method comparison | Follow-up: sampling density, intermediate powers and stronger curvature

The estimator and its graph restriction | Noisy circles with different sampling densities | Does a sparse graph give the same distances? | Two noisy arms with diffuse background points | How much does the first seed conceal? | Complete-graph distances without storing the graph | Sparse metric MDS with consistent Fermat targets | What the theory does and does not establish | Exact nearest neighbors without all-pairs distances | References

Choose a starting point | A first graph | Constructing a standard graph | Conventions that affect your choice | A common graph object | Neighborhood sizes and edge quantities | Connectivity, stages and cost | Distances and stored routes | Positive spectra and spectral coordinates | Plotting a graph and reusing its layout | Reuse an expensive computation | Function catalog | Graph construction and parameter sequences | Basic graphs and representation | Connectivity and graph editing | Paths and distances | Edge lengths and pruning | Diagnostics, endpoints and packing | Spectral methods and graph display | Synthetic geometry and embedding | Point sampling | Interactive graph reconstruction explorer | Object workflows and method help | Finding more help | Detailed help for this build

Build the optional backend once | Construct and inspect a graph | Numerical behavior and incomplete results | Resources and qualification

Choose a starting point | A first regression fit | Prediction and reusable fits | Refit and extract smoother matrices | Function catalog | Shared model operations | Local regression and prediction synchronization | Model assessment and uncertainty | Lifting trend filters | Graph spectral smoothing and graph trend filtering | From a constructed graph to a fitted response | Hessian-energy regression | Harmonic interpolation | Probability mass and subject occupation | Experimental transport methods | Synthetic datasets: specifications, responses, and reproducibility | Geometry constructors and helpers supplied by dgraphs | Sampling constructors supplied by dgraphs | Finding detailed help | Advanced controls without a new fitter

Choose a dataset | Provenance and scope | Gut counts | Valencia abundance data and saved assignments | Four-component data | Align data and metadata | Constructed edge cases | Reference and query | A static chart from the four-component data

Choose a starting point | A first view | Keep observations aligned | Function catalog | Point clouds and annotations | Graph preparation and plotting | Reusable color scales and legends | Geometric layers | Cameras and aspect ratios | Recorded-coordinate animation and export | Optional packages and detailed help

Watch a Sierpinski triangle unfold | Supply your own frames | Animate a changing 3D surface | From a paraboloid through a flat grid to a saddle | Export interactive HTML | Export a GIF | Control size and preserve diagnostic meaning

A sample from a saddle | Reusable numerical colors | Textbook-style axes and a z-up camera | A triangular mesh beneath the spheres | Groups and highlighting | Groups on the mesh-backed saddle | A gridded reference surface | Weighted graphs and geometric layers | Cameras, metadata, and export

A curve: angles, coordinates and a graph | A quadratic surface: parameter sampling and embedding | Chords, lifted segments and shortest paths | Random frames and single points | Explore quadratic geometry in 3D | Shape: flat, bowl, dome, cylinder, saddle and mixed terms | Sampling: domain, density, gaps and ordering | Placement: canonical, supplied and random frames, with offsets | Dimensions: a curve, multiple heights, a 3D latent domain and one point | Differential geometry: gradient, metric and area element | Inspect the graph and a lifted latent segment | A simplex with a lower-dimensional face | Choosing compatible sampling specifications | Reproducibility and continuation | Opting into the current R stream | Next steps

Part 1: Quick Start with Toy Data | L-infinity normalization | Dominance sample sets | Truncated dCSTs | Part 2: Gut Microbiome dCST Demonstration | Background | The data | Step 1: Quality filtering | Step 2: L-infinity normalization | Step 3: Depth-1 dCSTs | How sensitive is depth 1 to the support threshold? | Step 4: Depth-2 refinement | Dominance strength | dCST size distribution | Phenotype metadata | Limitations | Summary

Choose a recipe | Construct a point cloud | Share a scale and camera | Prepare a small embedded weighted graph | Record a short coordinate sequence | Save and clean up | Inspect the retinal bundle without refitting | Compare spatial extents

Load the prepared case study | Data lineage | Source and use terms | Shared categorical scales | Published UMAP as a point cloud | Compare the embeddings without edges | Add the symmetric kNN graph | Change the annotation, not the geometry | Interpretation and boundaries | Reproduction and provenance

Introduction | The Valencia 2k dataset | Reconstructing counts | $L^\infty$ normalization | Dominance sample sets: dominant species assignment | Depth-1 dCSTs | Concordance with Valencia CSTs | Depth-2 refinement | Concordance with Valencia sub-CSTs | The full pipeline | Landmark points | Summary | References

Overview | Construct candidate graph families | Inspect a parameter sequence | Convert and inspect a selected graph | Diagnose geodesic fidelity | Practical guidance