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).
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.
