Controllability of giant connected components in a directed network

Physical Review. E
Xueming LiuJianxi Gao

Abstract

When controlling a complex networked system it is not feasible to control the full network because many networks, including biological, technological, and social systems, are massive in size and complexity. But neither is it necessary to control the full network. In complex networks, the giant connected components provide the essential information about the entire system. How to control these giant connected components of a network remains an open question. We derive the mathematical expression of the degree distributions for four types of giant connected components and develop an analytic tool for studying the controllability of these giant connected components. We find that for both Erdős-Rényi (ER) networks and scale-free (SF) networks with p fraction of remaining nodes, the minimum driver node density to control the giant component first increases and then decreases as p increases from zero to one, showing a peak at a critical point p=p_{m}. We find that, for ER networks, the peak value of the driver node density remains the same regardless of its average degree 〈k〉 and that it is determined by p_{m}〈k〉. In addition, we find that for SF networks the minimum driver node densities needed to control the giant components of net...Continue Reading

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Citations

Mar 21, 2018·Scientific Reports·Xin-Jian XuLi-Jie Zhang
Sep 22, 2018·Briefings in Bioinformatics·Min LiFang-Xiang Wu
Feb 29, 2020·Scientific Reports·Giannis Moutsinas, Weisi Guo
Apr 9, 2021·Scientific Reports·Christopher BrissetteBoleslaw K Szymanski

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