A tool to detect the backbone in temporal networks

An efficient and fast tool to detect the backbone network in temporal networks. For accurate results, it should be applied to networks with at least 1,000 nodes.

The computational time is O(N_E I_{max}^2), where N_E are the number of unique edges in the network and I_{max} the maximum number of intervals. I_{max} can be computed as T (total time steps) divided by the minimum length of the interval, \Delta I_{min}.

For sparse networks (like most of the large networks), the computational time is O(N I_{max}^2)

How to install it

pip install TemporalBackbone

In order to run the library, additional packages should be installed

pip install wget 
wget https://raw.githubusercontent.com/matnado/TemporalBackbone/main/TemporalBackbone/requirements.txt
pip install -r requirements.txt

This implementation assumes that packages like copy, collections, and time are already present, because they cannot be installed via pip install.

How to run the package

import TemporalBackbone as TB

data = TB.Read_sample()
TB.Temporal_Backbone(data)

Input:

• df pandas dataframe with three columns: node1, node2, time (order is important)
• I_min minimum length of the interval, written in seconds: default 1 day or 60x60x24 seconds (time step is taken from the data)
• is_directed whether the network is directed or not: default True
• Bonferroni whether to use the Bonferroni correction: default True
• alpha threshold to determine the significance of a link: default 0.01

Output:

• list with the significant links

Please cite

The methodology is first introduced in Nadini, M., Bongiorno, C., Rizzo, A., & Porfiri, M. (2020). Detecting network backbones against time variations in node properties. Nonlinear Dynamics, 99(1), 855-878.

Then was deemed as appropriate for large temporal networks, having a good trade-off between false positives and false negatives. See Nadini, M., Rizzo, A., & Porfiri, M. (2020). Reconstructing irreducible links in temporal networks: which tool to choose depends on the network size. Journal of Physics: Complexity, 1(1), 015001.