On the Smallest Eigenvalue of Grounded Laplacian Matrices

Pirani, Mohammad; Sundaram, Shreyas

doi:10.1109/tac.2015.2444191

Cited by 61 publications

(76 citation statements)

References 34 publications

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“…In this section, we proceed to explore the correlation between TC and two network performance metrics, namely, the convergence rate of consensus and the network robustness, both of which are closely related to the spectra of 721. Since TC is derived from the normalised eigenvector of the perturbed Laplacian matrix, there are analytic connections between TC and network performances that are determined by the spectra of .…”

Section: Resultsmentioning

confidence: 99%

“…The smallest eigenvalue of (denoted by λ 1 in our discussion) provides us with the convergence rate of the consensus network influenced by the external input, on the other hand, λ 1 reflects how fast the diffusion of the external input (friendly or malicious, deterministic or stochastic) proceeds on the network722. Therefore, λ 1 can be regarded as a measure of spreading power of nodes in a consensus network from the perspective of the propagation efficiency of external inputs (refer to section 1 in Supplementary Information for details).…”

Section: Resultsmentioning

confidence: 99%

“…In addition to the network topology, the dynamics provides an alternative ingredient for identifying the role of nodes in a complex network. Recently, more links between centrality metrics and the network dynamics have been explored, such as in the context of percolation centrality5, control centrality6, and grounding centrality7, etc.…”

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confidence: 99%

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Inferring Centrality from Network Snapshots

Shao

Mesbahi

et al. 2017

Sci Rep

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The topology and dynamics of a complex network shape its functionality. However, the topologies of many large-scale networks are either unavailable or incomplete. Without the explicit knowledge of network topology, we show how the data generated from the network dynamics can be utilised to infer the tempo centrality, which is proposed to quantify the influence of nodes in a consensus network. We show that the tempo centrality can be used to construct an accurate estimate of both the propagation rate of influence exerted on consensus networks and the Kirchhoff index of the underlying graph. Moreover, the tempo centrality also encodes the disturbance rejection of nodes in a consensus network. Our findings provide an approach to infer the performance of a consensus network from its temporal data.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Inferring Centrality from Network Snapshots

Shao

Mesbahi

et al. 2017

Sci Rep

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“…Remark 8 When C = I d , the eigenvalue of L 22 with the smallest real part, denoted λ(L 22 ), governs the convergence rate of (5). Emerging results have studied how changes to network topology (including stubbornness b i ) impacts λ(L 22 ) [17,26], but it is not clear how the introduction of C = I d affects such results, and may be a future research direction.…”

Section: Remarkmentioning

confidence: 99%

Continuous-time opinion dynamics on multiple interdependent topics

Trinh

Lim

et al. 2020

Automatica

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In this paper, and inspired by the recent discrete-time model in [1,2], we study two continuous-time opinion dynamics models (Model 1 and Model 2) where the individuals discuss opinions on multiple logically interdependent topics. The logical interdependence between the different topics is captured by a "logic" matrix, which is distinct from the Laplacian matrix capturing interactions between individuals. For each of Model 1 and Model 2, we obtain a necessary and sufficient condition for the network to reach to a consensus on each separate topic. The condition on Model 1 involves a combination of the eigenvalues of the logic matrix and Laplacian matrix, whereas the condition on Model 2 requires only separate conditions on the logic matrix and Laplacian matrix. Further investigations of Model 1 yields two sufficient conditions for consensus, and allow us to conclude that one way to guarantee a consensus is to reduce the rate of interaction between individuals exchanging opinions. By placing further restrictions on the logic matrix, we also establish a set of Laplacian matrices which guarantee consensus for Model 1. The two models are also expanded to include stubborn individuals, who remain attached to their initial opinions. Sufficient conditions are obtained for guaranteeing convergence of the opinion dynamics system, with the final opinions generally being at a persistent disagreement. Simulations are provided to illustrate the results.

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“…There are many additional avenues of further exploration, such as the role of network topology [19,24] and design parameters k  , k h on the convergence rate. This was addressed by providing an iteration schedule to the nodes ahead of time so that all nodes can effectively perform updates synchronously.…”

Section: Discussionmentioning

confidence: 99%

An Algorithm for Accurate Distributed Time Synchronization in Mobile Wireless Sensor Networks from Noisy Difference Measurements

Liao¹,

Barooah

2016

Asian Journal of Control

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We propose a distributed algorithm for time synchronization in mobile wireless sensor networks. The problem of time synchronization is formulated as nodes estimating their skews and offsets from noisy difference measurements of offsets and logarithm of skews; the measurements acquired by time-stamped message exchanges between neighbors. The algorithm ensures that the estimation error is mean square convergent (variance converging to 0) under certain conditions. A sequence of scheduled update instants is used to meet the requirement of decreasing time-varying gains that need to be synchronized across nodes with unsynchronized clocks. Moreover, a modification on the algorithm is also presented to improve the initial convergence speed. Simulations indicate that highly accurate global time estimates can be achieved with the proposed algorithm for long time durations, while the errors in competing algorithms increase over time.where the scalar parameters u , u are called its skew (the relative speed of the clock with respect to t) and offset Manuscript

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On the Smallest Eigenvalue of Grounded Laplacian Matrices

Cited by 61 publications

References 34 publications

Inferring Centrality from Network Snapshots

Inferring Centrality from Network Snapshots

Continuous-time opinion dynamics on multiple interdependent topics

An Algorithm for Accurate Distributed Time Synchronization in Mobile Wireless Sensor Networks from Noisy Difference Measurements

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