Topological Data Analysis: Simplicial Complex

SimplicialComplex is a user-friendly Topological Data Analysis (TDA) package written entirely in R. While most TDA libraries (Dionysus, PHAT, GUDHI) are developed in Python and C++, implementing simplicial complexes natively in R makes them directly compatible with the rich ecosystem of statistical methods R already offers.

Features

• Simplicial complexes — build Vietoris–Rips complexes from point clouds, or define abstract simplicial complexes by hand.
• Topological invariants — faces, boundary matrices, Betti numbers, and the Euler characteristic.
• Persistent homology — filtrations, boundary-matrix reduction, persistence pairs, and persistence diagrams. Full worked examples in inst/example.
• Flood complex (in development) — a lightweight filtered complex on landmarks for large-scale persistent homology, following Graf et al. (NeurIPS 2025).

Playground

Try the interactive playground to get familiar with all the concepts used in TDA.

References

• Zomorodian, A., & Carlsson, G. (2004). Computing persistent homology. Proceedings of the Twentieth Annual Symposium on Computational Geometry, 347–356.
• Chazal, F., & Michel, B. (2021). An introduction to topological data analysis: Fundamental and practical aspects for data scientists. Frontiers in Artificial Intelligence, 4, 667963.
• Graf, F., Pellizzoni, P., Uray, M., Huber, S., & Kwitt, R. (2025). The Flood Complex: Large-scale persistent homology on millions of points. Advances in Neural Information Processing Systems, 38.