Python package to reconstruct and analyse delay functional networks from time series. It provides tools for data preparation and detrending, multiple connectivity measures (e.g. Granger causality, transfer entropy, correlations), optimal-lag network reconstruction, and network analysis.

Features

• Connectivity measures with hypothesis testing and optimal-lag reconstruction
• Network analysis: betweenness, eigenvector centrality, link density, transitivity, reciprocity, isolated nodes, global efficiency
• Null-model normalisation for metrics: report z-scores vs directed G(n,m) random graphs (igraph-based; binary-only; on-the-fly generation)
• Comprehensive documentation and examples
• Tested across multiple Python versions with high coverage

For details on how to use this package, see the Guide or the Documentation.

Setup

This package can be installed from PyPI using pip:

bash pip install delaynet # when public on PyPI

This will automatically install all the necessary dependencies as specified in the pyproject.toml file. It is recommended to use a virtual environment, e.g., using conda, mamba or micromamba (they can be used interchangeably).

bash micromamba create -n delay_net -c conda-forge python micromamba activate delay_net pip install delaynet # or `micromamba install delaynet` when on conda-forge

Quickstart

```python import numpy as np import delaynet as dn

Generate toy data: 5 nodes, 300 time points

rng = np.random.defaultrng(1520) data = rng.standardnormal((300, 5))

Compute a connectivity p-value and lag for one pair

pval, lag = dn.connectivity(data[:, 0], data[:, 1], metric="gc", lag_steps=10) print(f"GC p-value={pval:.3g}, best lag={lag}")

Reconstruct a delay network (p-value matrix and lag matrix)

weights, lags = dn.reconstructnetwork(data, connectivitymeasure="gc", lag_steps=5) print(weights.shape, lags.shape) ```

Development Setup

For development, we recommend using uv or micromamba to create a virtual environment. After cloning the repository, navigate to the root folder and create the environment. When using uv, the environment can be created with the following command:

bash uv sync

Or, if you prefer to use micromamba, with the desired Python version and the dependencies.

bash micromamba create -n delay_net -c conda-forge -f requirements.txt micromamba activate delay_net

Either way, using pip to install the package in editable mode will also install the development dependencies.

bash pip install -e ".[all]"

Or, to let micromamba handle the dependencies, use the requirements.txt file

bash micromamba install --file requirements.txt pip install --no-build-isolation --no-deps -e .

Now, the package can be imported and used in the python environment, from anywhere on the system if the environment is activated.

Set up Jupyter kernel

If you want to use delaynet with its environment delay_net in Jupyter, run:

bash pip install --user ipykernel python -m ipykernel install --user --name=delay_net

This allows you to run Jupyter with the kernel delay_net (Kernel > Change Kernel > im_env)

Acknowledgments

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 851255). This work was partially supported by the María de Maeztu project CEX2021-001164-M funded by the MICIU/AEI/10.13039/501100011033 and FEDER, EU.