network_control: A toolbox for implementing Network Control Theory analyses in python

Overview Documentation Status

Network Control Theory (NCT) is a branch of physical and engineering sciences that treats a network as a dynamical system. Generally, the system is controlled through signals that originate at a control point (or control points) and move through the network. In the brain, NCT models each region’s activity as a time-dependent internal state that is predicted from a combination of three factors: (i) its previous state, (ii) whole-brain structural connectivity, and (iii) external inputs. NCT enables asking a broad range of questions of a networked system that are highly relevant to network neuroscientists, such as: which regions are positioned such that they can efficiently distribute activity throughout the brain to drive changes in brain states? Do different brain regions control system dynamics in different ways? Given a set of control nodes, how can the system be driven to specific target state, or switch between a pair of states, by means of internal or external control input?

network_control is a Python toolbox that provides researchers with a set of tools to conduct some of the common NCT analyses reported in the literature. Below, we list select publications that serve as a primer for these tools and their use cases:

1. Gu, S., Pasqualetti, F., Cieslak, M. et al. Controllability of structural brain networks. Nature Communications (2015).

2. Gu, S., Betzel R. F., Mattar, M. G. et al. Optimal trajectories of brain state transitions. NeuroImage (2017).

3. Karrer, T. M., Kim, J. Z., Stiso, J. et al. A practical guide to methodological considerations in the controllability of structural brain networks. Journal of Neural Engineering (2020).

4. Kim, J. Z., & Bassett, D. S. Linear dynamics & control of brain networks. arXiv (2019).


Currently, network_control works with Python 3.6 and requires the following dependencies:

  • numpy (tested on 1.19.5), and

  • scipy (tested on 1.5.4)

There are some additional (optional) dependencies you can install (note, these are only used for i/o and plotting and only need to be installed if you want to run the notebooks in network_control/tests/):

  • pandas (tested on 1.1.5)

  • statsmodels (tested on 0.12.2)

  • matplotlib (tested on 3.3.4)

  • seaborn (tested on 0.11.1), and

  • jupyterlab (tested on 3.0.16)

Basic installation

Assuming you have Python 3.6 installed, you can install network_control by opening a terminal and running the following:

pip install network_control

What’s New

  • v0.0.4: initial package release for network_control

  • v0.0.5: added options for specifying timescales, integration function, gramian function, better estimation of the number of time points, and optimal energy example


If you have any questions, please contact Linden Parkes (, Jennifer Stiso ( or Jason Kim ( For questions or clarification about the theory pages of the documentation, please contact Jason Kim (