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From the website:

The GUDHI library is a generic open source C++ library, with a Python interface, for Topological Data Analysis (TDA) and Higher Dimensional Geometry Understanding. The library offers state-of-the-art data structures and algorithms to construct simplicial complexes and compute persistent homology.

The library comes with data sets, demos, examples and test suites.

Supported data types include:

Gudhi implements most representations of persistence diagrams such as:

Gudhi also implements various features and kernels for persistence diagrams such as:

Gudhi has several convenience methods for working with persistence diagrams, distances, and for plotting.

complex/alpha complex/cover-mapper complex/cubical complex/rips complex/rips-weighted complex/simplicial complex/tangential complex/witness custom/distance custom/filtration dist/bottleneck dist/wasserstein lang/c++ lang/python repr/atol repr/image repr/kernel repr/landscape repr/silhouette type/clustering type/persistence type/representative vis/barcode vis/density vis/diagram