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Register a new userImproving controllability of complex networks by rewiring links regularly
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Jinfa Wang
Publication date
2014
fields
Informatics Engineering
and research's language is
English
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Network science have constantly been in the focus of research for the last decade, with considerable advances in the controllability of their structural. However, much less effort has been devoted to study that how to improve the controllability of complex networks. In this paper, a new algorithm is proposed to improve the controllability of complex networks by rewiring links regularly which transforms the network structure. Then it is demonstrated that our algorithm is very effective after numerical simulation experiment on typical network models (Erdos-Renyi and scale-free network). We find that our algorithm is mainly determined by the average degree and positive correlation of in-degree and out-degree of network and it has nothing to do with the network size. Furthermore, we analyze and discuss the correlation between controllability of complex networks and degree distribution index: power-law exponent and heterogeneity
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Sun et al. provided an insightful comment arXiv:1108.5739v1 on our manuscript entitled Controllability of Complex Networks with Nonlinear Dynamics on arXiv. We agree on their main point that linearization about locally desired states can be violated in general by the breakdown of local control of the linearized complex network with nonlinear state. Therefore, we withdraw our manuscript. However, other than nonlinear dynamics, our claim that a single-node-control can fully control the general bidirectional/undirected linear network with 1D self-dynamics is still valid, which is similar to (but different from) the conclusion of arXiv:1106.2573v3 that all-node-control with a single signal can fully control any direct linear network with nodal-dynamics (1D self-dynamics).
In this paper, we investigate the linear controllability framework for complex networks from a physical point of view. There are three main results. (1) If one applies control signals as determined from the structural controllability theory, there is a high probability that the control energy will diverge. Especially, if a network is deemed controllable using a single driving signal, then most likely the energy will diverge. (2) The energy required for control exhibits a power-law scaling behavior. (3) Applying additional control signals at proper nodes in the network can reduce and optimize the energy cost. We identify the fundamental structures embedded in the network, the longest control chains, which determine the control energy and give rise to the power-scaling behavior. (To our knowledge, this was not reported in any previous work on control of complex networks.) In addition, the issue of control precision is addressed. These results are supported by extensive simulations from model and real networks, physical reasoning, and mathematical analyses. Notes on the submission history of this work: This work started in late 2012. The phenomena of power-law energy scaling and energy divergence with a single controller were discovered in 2013. Strategies to reduce and optimize control energy was articulated and tested in 2013. The senior co-author (YCL) gave talks about these results at several conferences, including the NETSCI 2014 Satellite entitled Controlling Complex Networks on June 2, 2014. The paper was submitted to PNAS in September 2014 and was turned down. It was revised and submitted to PRX in early 2015 and was rejected. After that it was revised and submitted to Nature Communications in May 2015 and again was turned down.
We study localization properties of principal eigenvector (PEV) of multilayer networks. Starting with a multilayer network corresponding to a delocalized PEV, we rewire the network edges using an optimization technique such that the PEV of the rewired multilayer network becomes more localized. The framework allows us to scrutinize structural and spectral properties of the networks at various localization points during the rewiring process. We show that rewiring only one-layer is enough to attain a multilayer network having a highly localized PEV. Our investigation reveals that a single edge rewiring of the optimized multilayer network can lead to the complete delocalization of a highly localized PEV. This sensitivity in the localization behavior of PEV is accompanied by a pair of almost degenerate eigenvalues. This observation opens an avenue to gain a deeper insight into the origin of PEV localization of networks. Furthermore, analysis of multilayer networks constructed using real-world social and biological data show that the localization properties of these real-world multilayer networks are in good agreement with the simulation results for the model multilayer network. The study is relevant to applications that require understanding propagation of perturbation in multilayer networks.
We study the extreme events taking place on complex networks. The transport on networks is modelled using random walks and we compute the probability for the occurance and recurrence of extreme events on the network. We show that the nodes with smaller number of links are more prone to extreme events than the ones with larger number of links. We obtain analytical estimates and verify them with numerical simulations. They are shown to be robust even when random walkers follow shortest path on the network. The results suggest a revision of design principles and can be used as an input for designing the nodes of a network so as to smoothly handle an extreme event.
As a fundamental structural transition in complex networks, core percolation is related to a wide range of important problems. Yet, previous theoretical studies of core percolation have been focusing on the classical ErdH{o}s-Renyi random networks with Poisson degree distribution, which are quite unlike many real-world networks with scale-free or fat-tailed degree distributions. Here we show that core percolation can be analytically studied for complex networks with arbitrary degree distributions. We derive the condition for core percolation and find that purely scale-free networks have no core for any degree exponents. We show that for undirected networks if core percolation occurs then it is always continuous while for directed networks it becomes discontinuous when the in- and out-degree distributions are different. We also apply our theory to real-world directed networks and find, surprisingly, that they often have much larger core sizes as compared to random models. These findings would help us better understand the interesting interplay between the structural and dynamical properties of complex networks.
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