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Identifying multiple influential spreaders in complex networks based on spectral graph theory
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作者 崔东旭 何嘉林 +1 位作者 肖子飞 任卫平 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第9期603-610,共8页
One of the hot research topics in propagation dynamics is identifying a set of critical nodes that can influence maximization in a complex network.The importance and dispersion of critical nodes among them are both vi... One of the hot research topics in propagation dynamics is identifying a set of critical nodes that can influence maximization in a complex network.The importance and dispersion of critical nodes among them are both vital factors that can influence maximization.We therefore propose a multiple influential spreaders identification algorithm based on spectral graph theory.This algorithm first quantifies the role played by the local structure of nodes in the propagation process,then classifies the nodes based on the eigenvectors of the Laplace matrix,and finally selects a set of critical nodes by the constraint that nodes in the same class are not adjacent to each other while different classes of nodes can be adjacent to each other.Experimental results on real and synthetic networks show that our algorithm outperforms the state-of-the-art and classical algorithms in the SIR model. 展开更多
关键词 spectral graph theory Laplace matrix influence maximization multiple influential spreaders
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Nonsmooth critical point theory and applications to the spectral graph theory
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作者 Kung-Ching Chang Sihong Shao +1 位作者 Dong Zhang Weixi Zhang 《Science China Mathematics》 SCIE CSCD 2021年第1期1-32,共32页
Existing critical point theories including metric and topological critical point theories are difficult to be applied directly to some concrete problems in particular polyhedral settings,because the notions of critica... Existing critical point theories including metric and topological critical point theories are difficult to be applied directly to some concrete problems in particular polyhedral settings,because the notions of critical sets could be either very vague or too large.To overcome these difficulties,we develop the critical point theory for nonsmooth but Lipschitzian functions defined on convex polyhedrons.This yields natural extensions of classical results in the critical point theory,such as the Liusternik-Schnirelmann multiplicity theorem.More importantly,eigenvectors for some eigenvalue problems involving graph 1-Laplacian coincide with critical points of the corresponding functions on polytopes,which indicates that the critical point theory proposed in the present paper can be applied to study the nonlinear spectral graph theory. 展开更多
关键词 critical point theory nonsmooth analysis combinatorial optimization POLYTOPE spectral graph theory
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Cheeger's cut, maxcut and the spectral theory of1-Laplacian on graphs 被引量:1
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作者 CHANG KungChing SHAO SiHong ZHANG Dong 《Science China Mathematics》 SCIE CSCD 2017年第11期1963-1980,共18页
This is primarily an expository paper surveying up-to-date known results on the spectral theory of1-Laplacian on graphs and its applications to the Cheeger cut, maxcut and multi-cut problems. The structure of eigenspa... This is primarily an expository paper surveying up-to-date known results on the spectral theory of1-Laplacian on graphs and its applications to the Cheeger cut, maxcut and multi-cut problems. The structure of eigenspace, nodal domains, multiplicities of eigenvalues, and algorithms for graph cuts are collected. 展开更多
关键词 spectral graph theory Laplacian graph cut optimization critical point theory
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Spectral Gap of the Largest Eigenvalue of the Normalized Graph Laplacian
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作者 Jürgen Jost Raffaella Mulas Florentin Münch 《Communications in Mathematics and Statistics》 SCIE 2022年第3期371-381,共11页
We offer a new method for proving that the maxima eigenvalue of the normalized graph Laplacian of a graph with n vertices is at least n+1/n−1 provided the graph is not complete and that equality is attained if and onl... We offer a new method for proving that the maxima eigenvalue of the normalized graph Laplacian of a graph with n vertices is at least n+1/n−1 provided the graph is not complete and that equality is attained if and only if the complement graph is a single edge or a complete bipartite graph with both parts of size n−1/2.With the same method,we also prove a new lower bound to the largest eigenvalue in terms of the minimum vertex degree,provided this is at most n−1/2. 展开更多
关键词 spectral graph theory Normalized Laplacian Largest eigenvalue Sharp bounds
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THE 1-LAPLACIAN CHEEGER CUT: THEORY AND ALGORITHMS 被引量:2
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作者 K.C. Chang Sihong Shao Dong Zhang 《Journal of Computational Mathematics》 SCIE CSCD 2015年第5期443-467,共25页
This paper presents a detailed review of both theory and algorithms for the Cheeger cut based on the graph 1-Laplacian. In virtue of the cell structure of the feasible set, we propose a cell descend (CD) framework f... This paper presents a detailed review of both theory and algorithms for the Cheeger cut based on the graph 1-Laplacian. In virtue of the cell structure of the feasible set, we propose a cell descend (CD) framework for achieving the Cheeger cut. While plugging the relaxation to guarantee the decrease of the objective value in the feasible set, from which both the inverse power (IP) method and the steepest descent (SD) method can also be recovered, we are able to get two specified CD methods. Comparisons of all these methods are conducted on several typical graphs. 展开更多
关键词 spectral graph theory spectral clustering 1-Laplace operator graph Lapla-cian Eigenvalue problems Cheeger constant graph cut Optimization CONVERGENCE
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Non-bipartite Graphs with Third Largest Laplacian Eigenvalue Less Than Three
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作者 Xiao Dong ZHANG Rong LUO 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2006年第3期917-934,共18页
All bipartite graphs whose third largest Laplacian eigenvalue is less than 3 have been characterized by Zhang. In this paper, all connected non-bipartite graphs with third largest Laplacian eigenvalue less than three ... All bipartite graphs whose third largest Laplacian eigenvalue is less than 3 have been characterized by Zhang. In this paper, all connected non-bipartite graphs with third largest Laplacian eigenvalue less than three are determined. 展开更多
关键词 spectral graph theory Laplacian eigenvalue forbidden subgraph
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GRAPHS CHARACTERIZED BY LAPLACIAN EIGENVALUES 被引量:2
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作者 ZHANGXIAODONG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2004年第1期103-110,共8页
This paper characterizes all connected graphs with exactly two Laplacian eigenval-ues greater than two and all connected graphs with exactly one Laplacian eigenvalue greater than three.
关键词 graphs spectral theory Laplacian eigenvalue Forbidden graph
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CONVERGENCE OF A CLASS OF MULTI-AGENT SYSTEMS IN PROBABILISTIC FRAMEWORK 被引量:9
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作者 Gongguo TANG Lei GUO 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2007年第2期173-197,共25页
Multi-agent systems arise from diverse fields in natural and artificial systems, and a basic problem is to understand how locally interacting agents lead to collective behaviors (e.g., synchronization) of the overal... Multi-agent systems arise from diverse fields in natural and artificial systems, and a basic problem is to understand how locally interacting agents lead to collective behaviors (e.g., synchronization) of the overall system. In this paper, we will consider a basic class of multi-agent systems that are described by a simplification of the well-known Vicsek model. This model looks simple, but the rigorous theoretical analysis is quite complicated, because there are strong nonlinear interactions among the agents in the model. In fact, most of the existing results on synchronization need to impose a certain connectivity condition on the global behaviors of the agents' trajectories (or on the closed-loop dynamic neighborhood graphs), which are quite hard to verify in general. In this paper, by introducing a probabilistic framework to this problem, we will provide a complete and rigorous proof for the fact that the overall multi-agent system will synchronize with large probability as long as the number of agents is large enough. The proof is based on a detailed analysis of both the dynamical properties of the nonlinear system evolution and the asymptotic properties of the spectrum of random geometric graphs. 展开更多
关键词 CONNECTIVITY large deviation local interaction rules multi-agent systems random geometric graph spectral graph theory SYNCHRONIZATION Vicsek model
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