Publication Results Recreated with netcontrolz

We have made an effort to recreate the main results of many papers in the network control literature. These have been selected both opportunistically (which are easier, immediate, etc) and also based on need. We endeavor to continue adding to this list over time. Many results rely on large datasets or large-scale computations. In these examples we select networks and dataset sizes that give reasonable computation time, while still capturing the main idea of the methods and results. Please feel free to submit suggestions or contribute code that will recreate the results of your own papers (send these to

We hope these files will also serve as a useful tutorial to get started with netcontrolz. The scripts that reproduce the publication results are located under the pubs directory within the netcontrolz repository.

Thomas et al, Complex Networks (2016)

Jijju Thomas, Supratim Ghosh, Deven Parek, Derek Ruths, Justin Ruths. Robustness of Network Controllability to Degree-Based Edge Attacks. Complex Networks & Their Applications V, 2016.

This paper characterizes the robustness properties of Erdos-Renyi and Barabasi-Albert random network models to various types of degree-based edge attacks as well as to random edge failure.

Abstract: We analyze the tolerance of network controllability to degree-based edge attacks as well as random edge failure. In particular, we leverage both control-based and reachability-based robustness metrics to investigate the case when a fixed number of controls are allowed to change locations following each attack. This ability to change the locations of controls models the more realistic scenario in which operators may have a fixed budget of resources but that these resources can be redeployed in response to attacks on the system. We also identify that the most potent targeted attack for network controllability selects edges (on average) based on betweenness centrality.

Yan et al, Nature Physics (2015)

Gang Yan, Georgios Tsekenis, Baruch Barzel, Jean-Jacques Slotine, Yang-Yu Liu, Albert-Laszlo Barabasi. Spectrum of controlling and observing complex networks. Nature Physics 11, 779–786 (2015).

This paper constructs the distribution of energies corresponding to the infinite horizon controllability Gramian. It observes largely scale-free distributions of energies when one or all nodes are driven by an external control(s). When an intermediate fraction of nodes is controlled, multi-peak distributions are observed and a gap between distinct bands of energies arises.

Abstract: Recent studies have made important advances in identifying sensor or driver nodes, through which we can observe or control a complex system. But the observational uncertainty induced by measurement noise and the energy required for control continue to be significant challenges in practical applications. Here we show that the variability of control energy and observational uncertainty for different directions of the state space depend strongly on the number of driver nodes. In particular, we find that if all nodes are directly driven, control is energetically feasible, as the maximum energy increases sublinearly with the system size. If, however, we aim to control a system through a single node, control in some directions is energetically prohibitive, increasing exponentially with the system size. For the cases in between, the maximum energy decays exponentially when the number of driver nodes increases. We validate our findings in several model and real networks, arriving at a series of fundamental laws to describe the control energy that together deepen our understanding of complex systems.

Ruths & Ruths, Science (2014)

Justin Ruths and Derek Ruths. Control Profiles of Complex Networks. Science, 343(6177), 1373-1376 (2014).

The paper shows that the correlation between the minimal number of controls required to guarantee controllability and the degree distribution is mainly due to the number of sources and sinks in a network. The paper also presents a new statistic, the control profile, which categorizes networks into three groups, which correspond to the three components of the control profile.

Abstract: Studying the control properties of complex networks provides insight into how designers and engineers can influence these systems to achieve a desired behavior. Topology of a network has been shown to strongly correlate with certain control properties; here we uncover the fundamental structures that explain the basis of this correlation. We develop the control profile, a statistic that quantifies the different proportions of control-inducing structures present in a network. We find that standard random network models do not reproduce the kinds of control profiles that are observed in real-world networks. The profiles of real networks form three well-defined clusters that provide insight into the high-level organization and function of complex systems.

Yan et al, Physical Review Letters (2012)

Gang Yan, Jie Ren, Ying-Cheng Lai, Choy-Heng Lai, and Baowen Li. Controlling Complex Networks: How Much Energy Is Needed? Phys. Rev. Lett. 108, 218703 (2012).

Abstract: The outstanding problem of controlling complex networks is relevant to many areas of science and engineering, and has the potential to generate technological breakthroughs as well. We address the physically important issue of the energy required for achieving control by deriving and validating scaling laws for the lower and upper energy bounds. These bounds represent a reasonable estimate of the energy cost associated with control, and provide a step forward from the current research on controllability toward ultimate control of complex networked dynamical systems.