Coherence analysis of a class of weighted networks

Dai, Meifeng; He, Jiaojiao; Zong, Yue; Ju, Tingting; Sun, Yu; Su, Weiyi

doi:10.1063/1.4997059

Cited by 29 publications

(7 citation statements)

References 26 publications

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“…Existing studies have demonstrated that calculations of the Laplacian eigenvalues face an enormous challenge because the eigenvalues are dominated by the network topology [9][10][11]. It is of interest to explore diverse methods to reveal the correlation between the topology and the coherence [12,13]. Particularly, for some fractal networks [14,15], such as Koch networks [16], Vicsek fractals [1], Sierpiński graphs [17], are all good candidate network models to derive an exact scaling of network coherence regarding the network size.…”

Section: Introductionmentioning

confidence: 99%

Topology design for leader-follower coherence in noisy asymmetric networks

Chen¹,

Sun²,

Wang³

2022

Phys. Scr.

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In this paper, we aim to study the effect of the leader's positions in leader-follower coherence quantified by the spectrum in noisy asymmetric networks with a set of hub nodes. In order to compare the impact of leader selection in different ways on the studied coherence, we choose a family of ring-trees networks to conveniently assign the leaders and hubs. Based on the regular network topology and matrix theories, we obtain analytical solutions for the leader-follower coherence regarding network parameters and the number of leaders. Using these expressions, we then obtain exact relations among the coherences and show that the leader's positions and network parameters have a profound impact on the coherence. More specifically, the network with one hub displays better coherence than the networks with two hubs. In addition, two adjacent and nonadjacent hubs lead to distinct performance of leader-follower consensus dynamics that depends on network parameters and assigned leaders in the ring or the tree network.

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Section: Introductionmentioning

confidence: 99%

Topology design for leader-follower coherence in noisy asymmetric networks

Chen¹,

Sun²,

Wang³

2022

Phys. Scr.

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“…In [10], Hong et al investigated a relation between the coherence and the number of initial nodes and showed the consensus bears better with a smaller number of initial nodes. Dai et al obtained the scalings of first-and second-order coherence for a family of weighted networks and found that the scalings obey different laws with a range of weight factors [11].…”

Section: Introductionmentioning

confidence: 99%

Leader selection for coherence in symmetric and asymmetric trees

Sun¹,

Li²,

Zheng³

2021

J. Stat. Mech.

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This paper studies consensus dynamics in symmetric and asymmetric trees with leader selection under additive noise environment, which is characterized as leader-follower coherence determined by the spectrum. In order to compare the effect of the leader's positions on the coherence, we choose a treelike network model and employ three different ways to assign the leaders. Based on the tree construction, we obtain exact solutions for the leader-follower coherence depending on the number of leaders and network parameters. We then show that the consensus in symmetric and asymmetric trees becomes better with an increasing number of leaders. When the number of leaders and network parameters satisfy certain conditions, the leader's positions and topological structures have a profound impact on the coherence.

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“…This concept of the network coherence helps to study the relationship between the Laplacian eigenvalues and network consistency. Great progress has been made for some special networks such as Vicsek fractals [10], tree-like networks [11], Sierpiński graphs [18] and weighted networks [19]. Many works have been devoted to studying the network coherence.…”

Section: Introductionmentioning

confidence: 99%

Network Coherence in a Family of Book Graphs

Chen¹,

Sun

2020

Front. Phys.

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In this paper, we study network coherence characterizing the consensus behaviors with additive noise in a family of book graphs. It is shown that the network coherence is determined by the eigenvalues of the Laplacian matrix. Using the topological structures of book graphs, we obtain recursive relationships for the Laplacian matrix and Laplacian eigenvalues and further derive exact expressions of the network coherence. Finally, we illustrate the robustness of network coherence under the graph parameters and show that the parameters have distinct effects on the coherence.

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Coherence analysis of a class of weighted networks

Cited by 29 publications

References 26 publications

Topology design for leader-follower coherence in noisy asymmetric networks

Topology design for leader-follower coherence in noisy asymmetric networks

Leader selection for coherence in symmetric and asymmetric trees

Network Coherence in a Family of Book Graphs

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