# Higra: Hierarchical Graph Analysis
[](https://perretb.visualstudio.com/AzurePipelines/_build/latest?definitionId=2&branchName=master)
[](https://ci.appveyor.com/project/PerretB/higra-21ed3)
[](https://codecov.io/gh/higra/Higra)
[](https://higra.readthedocs.io/en/stable/?badge=stable)
Higra is a C++/Python library for efficient sparse graph analysis with a special focus on hierarchical methods. Some of the main features are:
- efficient methods and data structures to handle the dual representations of hierarchical clustering: trees (dendrograms) and saliency maps (ultrametric distances);
- hierarchical clusterings: quasi-flat zone hierarchy, hierarchical watersheds, agglomerative clustering (single-linkage, average-linkage, complete-linkage, exponential-linkage, Ward, or user provided linkage rule), constrained connectivity hierarchy;
- component trees: min and max trees;
- manipulate and explore hierarchies: simplification, accumulators, cluster extraction, various attributes (size, volume, dynamics, perimeter, compactness, moments, etc.), horizontal and non-horizontal cuts, hierarchies alignment;
- optimization on hierarchies: optimal cuts, energy hierarchies;
- algorithms on graphs: accumulators, vertices and clusters dissimilarities, region adjacency graphs, minimum spanning trees and forests, watershed cuts;
- assessment: supervised assessment of graph clusterings and hierarchical clusterings;
- image toolbox: special methods for grid graphs, tree of shapes, hierarchical clustering methods dedicated to image analysis, optimization of Mumford-Shah energy.
Higra is thought for modularity, performance and seamless integration with classical data analysis pipelines. The data structures (graphs and trees) are decoupled from data (vertex and edge weights ) which are simply arrays ([xtensor](https://github.com/QuantStack/xtensor) arrays in C++ and [numpy](https://github.com/numpy/numpy) arrays in Python).
## Installation
The Python package can be installed with Pypi:
```bash
pip install higra
```
Supported systems:
- Python 3.9, 3.10, 3.11, 3.12, 3.13 (amd64)
- Linux 64 bits, macOS, Windows 64 bits (requires [Visual C++ Redistributable for Visual Studio 2015](https://support.microsoft.com/en-us/help/2977003/the-latest-supported-visual-c-downloads))
macOS ARM64 is currently only supported through conda ``conda install higra -c conda-forge``
## Documentation
[https://higra.readthedocs.io/](https://higra.readthedocs.io/)
### Demonstration and tutorials
A collection of demonstration notebooks is available in the [documentation](https://higra.readthedocs.io/en/stable/notebooks.html).
Notebooks are stored in a dedicated repository [Higra-Notebooks](https://github.com/higra/Higra-Notebooks).
### Code samples
This example demonstrates the construction of a single-linkage hierarchical clustering and its simplification by a cluster size criterion.
[](https://github.com/higra/Higra-Notebooks/blob/master/Illustrations%20of%20SoftwareX%202019%20article.ipynb)
This example demonstrates the use of hierarchical clustering for image filtering.
[](https://github.com/higra/Higra-Notebooks/blob/master/Illustrations%20of%20SoftwareX%202019%20article.ipynb)
## Developing C++ extensions
While Higra provides many vectorized operators to implement algorithms efficiently in Python, it is possible that
some operations cannot be done efficiently in Python.
In such case, the [Higra-cppextension-cookiecutter](https://github.com/higra/Higra-cppextension-cookiecutter) enables
to easily setup and generate c++ extension using Higra with Python bindings.
## License and how-to cite
The license [Cecill-B](http://www.cecill.info/licences/Licence_CeCILL-B_V1-en.txt) is fully compatible with BSD-like licenses (BSD, X11, MIT) with an attribution requirement.
The recommended way to give attribution is by citing the following presentation article:
> B. Perret, G. Chierchia, J. Cousty, S.J. F. Guimarães, Y. Kenmochi, L. Najman, [Higra: Hierarchical Graph Analysis](http://www.sciencedirect.com/science/article/pii/S235271101930247X), SoftwareX, Volume 10, 2019. DOI: 10.1016/j.softx.2019.100335
<details>
<summary><b>Bibtex</b></summary>
@article{PCCGKN:softwarex2019,
title = "Higra: Hierarchical Graph Analysis",
journal = "SoftwareX",
volume = "10",
pages = "1--6",
year = "2019",
issn = "2352-7110",
doi = "10.1016/j.softx.2019.100335",
author = "B. Perret and G. Chierchia and J. Cousty and S.J. F. Guimar\~{a}es and Y. Kenmochi and L. Najman",
}
</details>
## Third-party libraries
Higra bundles several third-party libraries (inside the `lib` folder):
- [pybind11](https://github.com/pybind/pybind11) helps to create Python bindings of c++ methods and classes - [BSD-style license](https://github.com/pybind/pybind11/blob/master/LICENSE)
- [xtensor](https://github.com/QuantStack/xtensor) (with [xtl](https://github.com/QuantStack/xtl), [xsimd](https://github.com/QuantStack/xsimd), and [xtensor-python](https://github.com/QuantStack/xtensor-python) provides `numpy` like arrays for c++ with seamless integration with Python - all under the [BSD-3-Clause license](https://github.com/QuantStack/xtensor/blob/master/LICENSE)
- [Catch2](https://github.com/catchorg/Catch2) is a unit test framework - [Boost Software License 1.0](https://github.com/catchorg/Catch2/blob/master/LICENSE.txt)
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"description": "\n\n# Higra: Hierarchical Graph Analysis\n\n[](https://perretb.visualstudio.com/AzurePipelines/_build/latest?definitionId=2&branchName=master)\n[](https://ci.appveyor.com/project/PerretB/higra-21ed3)\n[](https://codecov.io/gh/higra/Higra)\n[](https://higra.readthedocs.io/en/stable/?badge=stable)\n\nHigra is a C++/Python library for efficient sparse graph analysis with a special focus on hierarchical methods. Some of the main features are:\n\n- efficient methods and data structures to handle the dual representations of hierarchical clustering: trees (dendrograms) and saliency maps (ultrametric distances);\n- hierarchical clusterings: quasi-flat zone hierarchy, hierarchical watersheds, agglomerative clustering (single-linkage, average-linkage, complete-linkage, exponential-linkage, Ward, or user provided linkage rule), constrained connectivity hierarchy;\n- component trees: min and max trees;\n- manipulate and explore hierarchies: simplification, accumulators, cluster extraction, various attributes (size, volume, dynamics, perimeter, compactness, moments, etc.), horizontal and non-horizontal cuts, hierarchies alignment;\n- optimization on hierarchies: optimal cuts, energy hierarchies;\n- algorithms on graphs: accumulators, vertices and clusters dissimilarities, region adjacency graphs, minimum spanning trees and forests, watershed cuts;\n- assessment: supervised assessment of graph clusterings and hierarchical clusterings;\n- image toolbox: special methods for grid graphs, tree of shapes, hierarchical clustering methods dedicated to image analysis, optimization of Mumford-Shah energy.\n\nHigra is thought for modularity, performance and seamless integration with classical data analysis pipelines. The data structures (graphs and trees) are decoupled from data (vertex and edge weights ) which are simply arrays ([xtensor](https://github.com/QuantStack/xtensor) arrays in C++ and [numpy](https://github.com/numpy/numpy) arrays in Python).\n\n## Installation\n\nThe Python package can be installed with Pypi:\n\n```bash\npip install higra\n```\n\nSupported systems: \n\n - Python 3.9, 3.10, 3.11, 3.12, 3.13 (amd64)\n - Linux 64 bits, macOS, Windows 64 bits (requires [Visual C++ Redistributable for Visual Studio 2015](https://support.microsoft.com/en-us/help/2977003/the-latest-supported-visual-c-downloads))\n\nmacOS ARM64 is currently only supported through conda ``conda install higra -c conda-forge``\n\n## Documentation\n\n[https://higra.readthedocs.io/](https://higra.readthedocs.io/)\n\n### Demonstration and tutorials\n\nA collection of demonstration notebooks is available in the [documentation](https://higra.readthedocs.io/en/stable/notebooks.html). \nNotebooks are stored in a dedicated repository [Higra-Notebooks](https://github.com/higra/Higra-Notebooks).\n\n### Code samples\n\nThis example demonstrates the construction of a single-linkage hierarchical clustering and its simplification by a cluster size criterion.\n\n[](https://github.com/higra/Higra-Notebooks/blob/master/Illustrations%20of%20SoftwareX%202019%20article.ipynb)\n\nThis example demonstrates the use of hierarchical clustering for image filtering.\n\n[](https://github.com/higra/Higra-Notebooks/blob/master/Illustrations%20of%20SoftwareX%202019%20article.ipynb)\n\n## Developing C++ extensions\n\nWhile Higra provides many vectorized operators to implement algorithms efficiently in Python, it is possible that\nsome operations cannot be done efficiently in Python. \nIn such case, the [Higra-cppextension-cookiecutter](https://github.com/higra/Higra-cppextension-cookiecutter) enables\nto easily setup and generate c++ extension using Higra with Python bindings.\n\n## License and how-to cite\n\nThe license [Cecill-B](http://www.cecill.info/licences/Licence_CeCILL-B_V1-en.txt) is fully compatible with BSD-like licenses (BSD, X11, MIT) with an attribution requirement.\n\nThe recommended way to give attribution is by citing the following presentation article:\n\n> B. Perret, G. Chierchia, J. Cousty, S.J. F. Guimar\u00e3es, Y. Kenmochi, L. Najman, [Higra: Hierarchical Graph Analysis](http://www.sciencedirect.com/science/article/pii/S235271101930247X), SoftwareX, Volume 10, 2019. DOI: 10.1016/j.softx.2019.100335\n\n<details> \n <summary><b>Bibtex</b></summary>\n \n @article{PCCGKN:softwarex2019,\n title = \"Higra: Hierarchical Graph Analysis\",\n journal = \"SoftwareX\",\n volume = \"10\",\n pages = \"1--6\",\n year = \"2019\",\n issn = \"2352-7110\",\n doi = \"10.1016/j.softx.2019.100335\",\n author = \"B. Perret and G. Chierchia and J. Cousty and S.J. F. Guimar\\~{a}es and Y. Kenmochi and L. 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