In this paper,we focus on inferring graph Laplacian matrix from the spatiotemporal signal which is defined as“time-vertex signal”.To realize this,we first represent the signals on a joint graph which is the Cartesia...In this paper,we focus on inferring graph Laplacian matrix from the spatiotemporal signal which is defined as“time-vertex signal”.To realize this,we first represent the signals on a joint graph which is the Cartesian product graph of the time-and vertex-graphs.By assuming the signals follow a Gaussian prior distribution on the joint graph,a meaningful representation that promotes the smoothness property of the joint graph signal is derived.Furthermore,by decoupling the joint graph,the graph learning framework is formulated as a joint optimization problem which includes signal denoising,timeand vertex-graphs learning together.Specifically,two algorithms are proposed to solve the optimization problem,where the discrete second-order difference operator with reversed sign(DSODO)in the time domain is used as the time-graph Laplacian operator to recover the signal and infer a vertex-graph in the first algorithm,and the time-graph,as well as the vertex-graph,is estimated by the other algorithm.Experiments on both synthetic and real-world datasets demonstrate that the proposed algorithms can effectively infer meaningful time-and vertex-graphs from noisy and incomplete data.展开更多
A weighted graph is a graph that has a numeric label associated with each edge, called the weight of edge. In many applications, the edge weights are usually represented by nonnegative integers or square matrices. The...A weighted graph is a graph that has a numeric label associated with each edge, called the weight of edge. In many applications, the edge weights are usually represented by nonnegative integers or square matrices. The weighted signless Laplacian matrix of a weighted graph is defined as the sum of adjacency matrix and degree matrix of same weighted graph. In this paper, a brief overview of the notation and concepts of weighted graphs that will be used throughout this study is given. In Section 2, the weighted signless Laplacian matrix of simple connected weighted graphs is considered, some upper bounds for the spectral radius of the weighted signless Laplacian matrix are obtained and some results on weighted and unweighted graphs are found.展开更多
The connectivity index was introduced by Randi´c(J.Am.Chem.Soc.97(23):6609–6615,1975)and was generalized by Bollobás and Erdös(Ars Comb.50:225–233,1998).It studies the branching property of graphs,and...The connectivity index was introduced by Randi´c(J.Am.Chem.Soc.97(23):6609–6615,1975)and was generalized by Bollobás and Erdös(Ars Comb.50:225–233,1998).It studies the branching property of graphs,and has been applied to studying network structures.In this paper we focus on the general sum-connectivity index which is a variant of the connectivity index.We characterize the tight upper and lower bounds of the largest eigenvalue of the general sum-connectivity matrix,as well as its spectral diameter.We show the corresponding extremal graphs.In addition,we show that the general sum-connectivity index is determined by the eigenvalues of the general sum-connectivity Laplacian matrix.展开更多
The signless Laplacian matrix of a graph is the sum of its diagonal matrix of vertex degrees and its adjacency matrix.Li and Feng gave some basic results on the largest eigenvalue and characteristic polynomial of adja...The signless Laplacian matrix of a graph is the sum of its diagonal matrix of vertex degrees and its adjacency matrix.Li and Feng gave some basic results on the largest eigenvalue and characteristic polynomial of adjacency matrix of a graph in 1979.In this paper,we translate these results into the signless Laplacian matrix of a graph and obtain the similar results.展开更多
In this paper,we give the upper bound and lower bound of k-th largest eigenvalue λ_κ of the Laplacian matrix of a graph G in terms of the edge number of G and the number of spanning trees of G.
In this paper, we found the bounds of the extreme eigenvalues of normalized Laplacian matrices and signless Laplacian matrices by using their traces. In addition, we found the bounds for k-th eigenvalues of normalized...In this paper, we found the bounds of the extreme eigenvalues of normalized Laplacian matrices and signless Laplacian matrices by using their traces. In addition, we found the bounds for k-th eigenvalues of normalized Laplacian matrix and signless Laplacian matrix.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.61966007)Key Laboratory of Cognitive Radio and Information Processing,Ministry of Education(No.CRKL180106,No.CRKL180201)+1 种基金Guangxi Key Laboratory of Wireless Wideband Communication and Signal Processing,Guilin University of Electronic Technology(No.GXKL06180107,No.GXKL06190117)Guangxi Colleges and Universities Key Laboratory of Satellite Navigation and Position Sensing.
文摘In this paper,we focus on inferring graph Laplacian matrix from the spatiotemporal signal which is defined as“time-vertex signal”.To realize this,we first represent the signals on a joint graph which is the Cartesian product graph of the time-and vertex-graphs.By assuming the signals follow a Gaussian prior distribution on the joint graph,a meaningful representation that promotes the smoothness property of the joint graph signal is derived.Furthermore,by decoupling the joint graph,the graph learning framework is formulated as a joint optimization problem which includes signal denoising,timeand vertex-graphs learning together.Specifically,two algorithms are proposed to solve the optimization problem,where the discrete second-order difference operator with reversed sign(DSODO)in the time domain is used as the time-graph Laplacian operator to recover the signal and infer a vertex-graph in the first algorithm,and the time-graph,as well as the vertex-graph,is estimated by the other algorithm.Experiments on both synthetic and real-world datasets demonstrate that the proposed algorithms can effectively infer meaningful time-and vertex-graphs from noisy and incomplete data.
文摘A weighted graph is a graph that has a numeric label associated with each edge, called the weight of edge. In many applications, the edge weights are usually represented by nonnegative integers or square matrices. The weighted signless Laplacian matrix of a weighted graph is defined as the sum of adjacency matrix and degree matrix of same weighted graph. In this paper, a brief overview of the notation and concepts of weighted graphs that will be used throughout this study is given. In Section 2, the weighted signless Laplacian matrix of simple connected weighted graphs is considered, some upper bounds for the spectral radius of the weighted signless Laplacian matrix are obtained and some results on weighted and unweighted graphs are found.
基金This work was supported by the Danish National Research Foundation and the National Science Foundation of China(No.61061130540)for the Sino-Danish Center for the Theory of Interactive Computation and by the Center for Research in Foundations of Electronic Markets(CFEM,supported by the Danish Strategic Research Council),within which this work was performedWe thank the anonymous reviewers for their thorough reviews and insightful comments,which helped us to improve the paper.
文摘The connectivity index was introduced by Randi´c(J.Am.Chem.Soc.97(23):6609–6615,1975)and was generalized by Bollobás and Erdös(Ars Comb.50:225–233,1998).It studies the branching property of graphs,and has been applied to studying network structures.In this paper we focus on the general sum-connectivity index which is a variant of the connectivity index.We characterize the tight upper and lower bounds of the largest eigenvalue of the general sum-connectivity matrix,as well as its spectral diameter.We show the corresponding extremal graphs.In addition,we show that the general sum-connectivity index is determined by the eigenvalues of the general sum-connectivity Laplacian matrix.
基金Foundation item： the National Natural Science Foundation of China （No. 10871204） Graduate Innovation Foundation of China University of Petroleum （No. S2008-26）.
文摘The signless Laplacian matrix of a graph is the sum of its diagonal matrix of vertex degrees and its adjacency matrix.Li and Feng gave some basic results on the largest eigenvalue and characteristic polynomial of adjacency matrix of a graph in 1979.In this paper,we translate these results into the signless Laplacian matrix of a graph and obtain the similar results.
基金the National Natural Science Foundation of China (Grant No.19971086) and the Doctoral Program Foundation of State Education Depa
文摘In this paper,we give the upper bound and lower bound of k-th largest eigenvalue λ_κ of the Laplacian matrix of a graph G in terms of the edge number of G and the number of spanning trees of G.
文摘In this paper, we found the bounds of the extreme eigenvalues of normalized Laplacian matrices and signless Laplacian matrices by using their traces. In addition, we found the bounds for k-th eigenvalues of normalized Laplacian matrix and signless Laplacian matrix.
