The FitnEss, The Relatedness and The other MetrIcs

fermi is a modular Python framework for analyzing the main Economic Complexity metrics and features. It provides tools to explore the hidden structure of economies through:

• 📊 Matrix preprocessing: raw cleaning, sparse conversion, Comparative advantage RCA/ICA, transformation and thresholding.
• 🧠 Fitness & complexity: compute Fitness, Complexity ECI, PCI and other metrics via multiple methods.
• 🌐 Relatedness metrics: product space, taxonomy, assist matrix.
• 📈 Prediction models: GDP forecasting, density models, XGBoost.
• ✅ Validation metrics: AUC, confusion matrix, prediction@k.

⚠️ Requires Python ≥ 3.0 To correnctly install and use the package, you need to have

numpy ≥ 1.24
pandas ≥ 1.5
scikit-learn ≥ 1.2
scipy ≥ 1.9
matplotlib ≥ 3.5
seaborn
bokeh ≥ 2.4
tqdm
networkx ≥ 2.6
bicm ≥ 3.3.1

To install fermi directly from PyPI in a virtual environment:

python -m venv fermi-env
source fermi-env/bin/activate  # or fermi-env\Scripts\activate on Windows
pip install fermi-cref

To use fermi on Colab, you can install it directly from PyPI with:

!pip install fermi-cref

The main module to generate an Economic Complexity object and initialize it (with a biadjacency matrix):

import fermi
myefc = fermi.efc()
myefc.load(my_biadjacency_matrix, *possible kwargs*)

To compute the Revealed Comparative Advantage (Balassa index) and binarize its value

myefc.compute_rca().binarize()

To compute the Fitness and the Complexity (using the original [Tacchella2012] algorithm)

fitness, complexity = myefc.get_fitness_complexity()

To compute the diversification and the ubiquity

div, ubi = myefc.get_diversification_ubiquity()

To compute the ECI index (using the eigenvalue method)

eci, pci = myefc.get_eci_pci()

The module to generate cooccurrences and similar relatedness measures is

myproj = fermi.RelatednessMetrics()
myproj.load(my_biadjacency_matrix, *possible kwargs*)

The cooccurrence can be evaluated using

relatedness = myproj.get_projection(projection_method="cooccurrence")
validated_relatedness, validated_values = myproj.get_bicm_projection(projection_method="cooccurrence", validation_method="fdr")

See a more detailed description in the API in the documentation.

If you use the fermi modules, please cite its location on Github https://github.com/EFC-data/fermi

[Tacchella2012] A. Tacchella, M. Cristelli, G. Caldarelli, A. Gabrielli, L. Pietronero , A New Metrics for Countries' Fitness and Products' Complexity, SciRep vol. 2, 723 (2012)

[Zaccaria2014] Zaccaria A, Cristelli M, Tacchella A, Pietronero L, How the Taxonomy of Products Drives the Economic Development of Countries, PLoS ONE, (2014), 9(12): e113770

[Tacchella2018] Tacchella A., Mazzilli D., Pietronero L. A dynamical systems approach to gross domestic product forecasting. Nature Phys 14, 861–865 (2018)

[Pugliese2019] Pugliese E., Cimini G., Patelli A. et al. Unfolding the innovation system for the development of countries: coevolution of Science, Technology and Production. Sci Rep vol. 9, 16440 (2019)

[Mazzilli2024] D Mazzilli, M S Mariani, F Morone and A Patelli, Equivalence between the Fitness-Complexity and the Sinkhorn-Knopp algorithms, J. Phys. Complex. 5 015010 (2024)

Authors: CREF Team

• Aurelio Patelli

• Riccardo Piombo

• Matteo Straccamore

• Filippo Santoro

• Valeria Secchini

• Lorenzo Buffa

• Daniele Cirulli

We gratefully acknowledge the invaluable contributions, support, and foundational code provided by Andrea Tacchella, Emanuele Pugliese, Dario Mazzilli, and Andrea Zaccaria.