Optimal synchronization on strongly connected directed networks

Brede, Markus

doi:10.1140/epjb/e2010-00016-7

Cited by 9 publications

(19 citation statements)

References 28 publications

(58 reference statements)

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“…Actually, the link swapping greedy algorithm has been commonly applied to achieve the optimal or near-optimal network functions such as node robustness [25], immunization [31], synchronization [32], and so on. In our case, although we cannot guarantee that this algorithm will obtain the global optimum, we have checked that the results from this algorithm are relatively stable in different swap trials.…”

Section: Networkmentioning

confidence: 99%

Enhancing network robustness against malicious attacks

2012

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In a recent work [Schneider et al., Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], the authors proposed a simple measure for network robustness under malicious attacks on nodes. Using a greedy algorithm, they found that the optimal structure with respect to this quantity is an onion structure in which high-degree nodes form a core surrounded by rings of nodes with decreasing degree. However, in real networks the failure can also occur in links such as dysfunctional power cables and blocked airlines. Accordingly, complementary to the node-robustness measurement (R(n)), we propose a link-robustness index (R(l)). We show that solely enhancing R(n) cannot guarantee the improvement of R(l). Moreover, the structure of an R(l)-optimized network is found to be entirely different from that of an onion network. In order to design robust networks that are resistant to a more realistic attack condition, we propose a hybrid greedy algorithm that takes both the R(n) and R(l) into account. We validate the robustness of our generated networks against malicious attacks mixed with both nodes and links failure. Finally, some economical constraints for swapping the links in real networks are considered, and significant improvement in both aspects of robustness is still achieved.

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Section: Networkmentioning

confidence: 99%

Enhancing network robustness against malicious attacks

2012

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“…It has been pointed out that these core nodes (i.e. high-degree nodes) are favorable for the network synchronizability [15]. In contrast, the RM method is unable to induce such an effective core; thus its synchronizability enhancement is only from the decreasing of the average shortest distance.…”

Section: Addingmentioning

confidence: 99%

“…Given a network, the coredistance is defined as the average shortest distance from the core node to all other nodes in this network. It was pointed out that the smaller the core-distance, the quicker the whole network converges to synchronization, since the core actually drives the whole network to the synchronized state [15]. The dependence of the core-distance on the number of added links in the directed WS networks is shown in figure 2(c).…”

Section: Addingmentioning

confidence: 99%

“…Understanding and controlling this collective dynamics is of both theoretical and practical significance [1,2]. Many methods have been proposed to enhance the network synchronizability, including the redistribution of the coupling strengths [3][4][5][6][7][8], the modification of the network structure [9][10][11][12][13], the flipping of link directionality [14][15][16][17] and so on. Each group of methods has its specific range of applications since different systems are under different technical constraints.…”

Section: Introductionmentioning

confidence: 99%

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Manipulating directed networks for better synchronization

2012

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In this paper, we studied the strategies to enhance synchronization on directed networks by manipulating a fixed number of links. We proposed a centrality-based manipulating (CBM) method, where the node centrality is measured by the well-known PageRank algorithm. Extensive numerical simulation on many modeled networks demonstrated that the CBM method is more effective in facilitating synchronization than the degree-based manipulating method and the random manipulating method for adding or removing links. The reason is that the CBM method can effectively narrow the incoming degree distribution and reinforce the hierarchical structure of the network. Furthermore, we apply the CBM method to the links rewiring procedure where at each step one link is removed and one new link is added. The CBM method helps to decide which links should be removed or added. After several steps, the resulting networks are very close to the optimal structure from the theoretical analysis and the evolutionary optimization algorithm. The numerical simulations on the Kuramoto model further demonstrate that our method has an advantage in shortening the convergence time to synchronization on directed networks.

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“…[15,16] improve the synchronizability by adding, removing and rewiring links in networks. The synchronizability is also enhanced by manipulating links based on evolutionary optimization algorithms [17][18][19]. Additionally, the synchronizability can be improved by properly assigning link directions [9,20].…”

Section: Introductionmentioning

confidence: 99%

Network skeleton for synchronization: Identifying redundant connections

Zhang

Zeng

2014

Physica A: Statistical Mechanics and its Applications

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h i g h l i g h t s• We find that many links in networks are actually redundant for synchronization.• The homogeneous networks have more redundant links than the heterogeneous networks.• The synchronization backbone is the minimal network to preserve synchronizability.• The results are confirmed by the Kuramoto model.Synchronization is an important dynamical process on complex networks with wide applications. In this paper, we design a greedy link removal algorithm and find that many links in networks are actually redundant for synchronization, i.e. the synchronizability of the network is hardly affected if these links are removed. Our analysis shows that homogeneous networks generally have more redundant links than heterogeneous networks. We denote the reduced network with the minimum number of links to preserve synchronizability (eigenratio of the Laplacian matrix) of the original network as the synchronization backbone. Simulating the Kuramoto model, we confirm that the network synchronizability is effectively preserved in the backbone. Moreover, the topological properties of the original network and backbone are compared in detail.

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Optimal synchronization on strongly connected directed networks

Cited by 9 publications

References 28 publications

Enhancing network robustness against malicious attacks

Enhancing network robustness against malicious attacks

Manipulating directed networks for better synchronization

Network skeleton for synchronization: Identifying redundant connections

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