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, Alpha, Cech, Witness, Cubical, and Flood 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, persistence diagrams, and persistence landscape.
• Statistical: Wasserstein distance & bottleneck distance were built in the latest version, with matching plot.
• Time/Step consideration: CROCKER and Zigzag persistence with plots.
• Discrete Morse Theory: Discrete Morse Vector Fields (DMVF) with plots.
• Laplacians: Basic Laplacian, persistent laplacian, and hodge laplacian
• Examples: Full worked examples in inst/example.

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.
• Otter, N., Porter, M. A., Tillmann, U., Grindrod, P., & Harrington, H. A. (2017). A roadmap for the computation of persistent homology. EPJ data science, 6(1), 17.
• Wei, X., & Wei, G. W. (2025). Persistent topological laplacians—a survey. Mathematics, 13(2), 208.
• Dey, T. K., & Wang, Y. (1945). Computational topology for data analysis. American history, 1861(1900).