Scale-Free Loopy Structure is Resistant to Noise in Consensus Dynamics in Complex Networks

Yi, Yuhao; Zhang, Zhongzhi; Patterson, Stacy

doi:10.1109/tcyb.2018.2868124

Cited by 44 publications

(26 citation statements)

References 75 publications

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“…Based on these classic models, researchers can predict the epidemic size, critical threshold, and associated critical phenomena. Besides, a large amount of improved models which capture the observed features like network topology [13,14], the state of the diseases [15], spatiality [16], and temporality [17,18] have been proposed.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Information-Driven Resource Allocation on the Propagation of Epidemic with Incubation Period

Zhu

Liu

Wang

et al. 2022

Preprint

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In the pandemic of COVID-19, there are exposed individuals who are infected but lack distinct clinical symptoms. In addition, the diffusion of related information drives aware individuals to spontaneously seek resources for protection. The special spreading characteristic and coevolution of different processes may induce unexpected spreading phenomena. Thus we construct a three-layered network framework to explore how information-driven resource allocation affects SEIS (Susceptible-Exposed-Infected-Susceptible) epidemic spreading. The analyses utilizing microscopic Markov chain approach reveal that the epidemic threshold depends on the topology structure of epidemic network, and the processes of information diffusion and resource allocation. Conducting extensive Monte Carlo simulations, we find some crucial phenomena in the coevolution of information diffusion, resource allocation and epidemic spreading. Firstly, when E-state (exposed state, without symptoms) individuals are infectious, long incubation period results in more E-state individuals than I-state (infected state, with obvious symptoms) individuals. Besides, when E-state individuals have strong or weak infectious capacity, increasing incubation period have an opposite effect on epidemic propagation. Secondly, the short incubation period induces the first-order phase transition. But enhancing the efficacy of resources would convert the phase transition to a second-order type. Finally, comparing the coevolution in networks with different topologies, we find setting the epidemic layer as scale-free network can inhibit the spreading of the epidemic.

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Section: Introductionmentioning

confidence: 99%

The Effect of Information-Driven Resource Allocation on the Propagation of Epidemic with Incubation Period

Zhu

Liu

Wang

et al. 2022

Preprint

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show abstract

“…dynamics [2], [3], [4] and bond percolation [5] on a graph. Concerning the Laplacian matrix, its smallest and largest nonzero eigenvalues are closely related to the time of convergence and delay robustness of the consensus problem [6]; all the nonzero eigenvalues determine the number of spanning trees [7] and the sum of resistance distances over all node pairs [8], [9], with the latter encoding the performance of different dynamical processes, such as the total hitting times of random walks [10], [11], [12] and robustness to noise in consensus problem [13], [14], [15].…”

Section: Introductionmentioning

confidence: 99%

Maximizing the Smallest Eigenvalue of Grounded Laplacian Matrix

Wang¹,

Zhou²,

Li³

et al. 2021

Preprint

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For a connected graph G = (V, E) with n nodes, m edges, and Laplacian matrix L, a grounded Laplacian matrix L(S) of G is a (n − k) × (n − k) principal submatrix of L, obtained from L by deleting k rows and columns corresponding to k selected nodes forming a set S ⊆ V . The smallest eigenvalue λ(S) of L(S) plays a pivotal role in various dynamics defined on G. For example, λ(S) characterizes the convergence rate of leader-follower consensus, as well as the effectiveness of a pinning scheme for the pinning control problem, with larger λ(S) corresponding to smaller convergence time or better effectiveness of a pinning scheme. In this paper, we focus on the problem of optimally selecting a subset S of fixed k ≪ n nodes, in order to maximize the smallest eigenvalue λ(S) of the grounded Laplacian matrix L(S). We show that this optimization problem is NP-hard and that the objective function is non-submodular but monotone. Due to the difficulty to obtain the optimal solution, we first propose a naïve heuristic algorithm selecting one optimal node at each time for k iterations. Then we propose a fast heuristic scalable algorithm to approximately solve this problem, using derivative matrix, matrix perturbations, and Laplacian solvers as tools. Our naïve heuristic algorithm takes Õ(knm) time, while the fast greedy heuristic has a nearly linear time complexity of Õ(km), where Õ(•) notation suppresses the poly(log n) factors. We also conduct numerous experiments on different networks sized up to one million nodes, demonstrating the superiority of our algorithm in terms of efficiency and effectiveness compared to baseline methods.

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“…e small-world characteristics of the network [3] and the scale-free characteristics [4] make some special nodes in the network have a great influence on the performance and structure of the network. ese nodes are called important nodes, and they are the core designers in the designer network.…”

Section: Introductionmentioning

confidence: 99%

A New Method of Identifying Core Designers and Teams Based on the Importance and Similarity of Networks

Liu

Huang

et al. 2021

Computational Intelligence and Neuroscience

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In the process of product collaborative design, the association between designers can be described by a complex network. Exploring the importance of the nodes and the rules of information dissemination in such networks is of great significance for distinguishing its core designers and potential designer teams, as well as for accurate recommendations of collaborative design tasks. Based on the neighborhood similarity model, combined with the idea of network information propagation, and with the help of the ReLU function, this paper proposes a new method for judging the importance of nodes—LLSR. This method not only reflects the local connection characteristics of nodes but also considers the trust degree of network propagation, and the neighbor nodes’ information is used to modify the node value. Next, in order to explore potential teams, an LA-LPA algorithm based on node importance and node similarity was proposed. Before the iterative update, all nodes were randomly sorted to get an update sequence which was replaced by the node importance sequence. When there are multiple largest neighbor labels in the propagation process, the label with the highest similarity is selected for update. The experimental results in the related networks show that the LLSR algorithm can better identify the core nodes in the network, and the LA-LPA algorithm has greatly improved the stability of the original LPA algorithm and has stably mined potential teams in the network.

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Scale-Free Loopy Structure is Resistant to Noise in Consensus Dynamics in Complex Networks

Cited by 44 publications

References 75 publications

The Effect of Information-Driven Resource Allocation on the Propagation of Epidemic with Incubation Period

The Effect of Information-Driven Resource Allocation on the Propagation of Epidemic with Incubation Period

Maximizing the Smallest Eigenvalue of Grounded Laplacian Matrix

A New Method of Identifying Core Designers and Teams Based on the Importance and Similarity of Networks

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