Generating complex networks with time-to-control communities.

Guilherme Ramos,Sérgio Pequito

doi:10.1371/journal.pone.0236753

Guilherme Ramos, Sérgio Pequito

Open Access

https://doi.org/10.1371/journal.pone.0236753

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Journal: PloS one	Publication Date: Aug 12, 2020
Citations: 4	License type: CC BY 4.0

Affiliation: University of Porto, Rensselaer Polytechnic Institute

Abstract

Dynamical networks are pervasive in a multitude of natural and human-made systems. Often, we seek to guarantee that their state is steered to the desired goal within a specified number of time steps. Different network topologies lead to implicit trade-offs between the minimum number of driven nodes and the time-to-control. In this study, we propose a generative model to create artificial dynamical networks with trade-offs similar to those of real networks. Remarkably, we show that several centrality and non-centrality measures are not necessary nor sufficient to explain the trade-offs, and as a consequence, commonly used generative models do not suffice to capture the dynamical properties under study. Therefore, we introduce the notion of time-to-control communities, that combine networks’ partitions and degree distributions, which is crucial for the proposed generative model. We believe that the proposed methodology is crucial when invoking generative models to investigate dynamical network properties across science and engineering applications. Lastly, we provide evidence that the proposed generative model can generate a variety of networks with statistically indiscernible trade-offs (i.e., the minimum number of driven nodes vs. the time-to-control) from those steaming from real networks (e.g., neural and social networks).

Highlights

Unveiling the nature of dynamical and controllability properties of complex networks through their structure is key to the design of networks with desirable properties
In the quest to overcome the limitations of current generative models, we propose a generative model to create artificial dynamical networks with similar actuation spectra to those of real networks
We introduce the notion of time-to-control communities that combine networks’ partitions and degree distributions that is key for the proposed generative model

Summary

Introduction

Unveiling the nature of dynamical and controllability properties of complex networks through their structure is key to the design of networks with desirable properties. These complex systems are present in nature, society, and technology. Controllability ascertains that a network’s state can be attained within as much time as the network size. It is well-known that to guarantee the controllability of a network the minimum number of driven nodes is characterized to a certain extent by the degree distribution of the network [2, 3].

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Conclusion