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Automatica, ISSN 0005-1098, 05/2019, Volume 103, pp. 374 - 378
This paper provides a construction method of the nearest graph Laplacian to a matrix identified from measurement data of graph Laplacian dynamics that include... 
Data-driven modeling | Graph Laplacian | Convex optimization | SYNCHRONIZATION | DYNAMICS | NETWORKS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC
Journal Article
Automatica, ISSN 0005-1098, 06/2013, Volume 49, Issue 6, pp. 1900 - 1906
The paper introduces complex-valued Laplacians for graphs whose edges are attributed with complex weights and studies the leader–follower formation problem... 
Formations | Stability | Complex Laplacian | Multi-agent systems | EIGENVALUE PROBLEMS | STABILIZATION | PERSISTENCE | NETWORKS | STRATEGIES | GRAPHS | ENGINEERING, ELECTRICAL & ELECTRONIC | RIGIDITY | SYSTEMS | VEHICLE FORMATIONS | AUTOMATION & CONTROL SYSTEMS | COOPERATIVE CONTROL | Algorithms | Computer Science | Automatic Control Engineering
Journal Article
IEEE Transactions on Neural Networks and Learning Systems, ISSN 2162-237X, 10/2015, Volume 26, Issue 10, pp. 2261 - 2274
Journal Article
IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 03/2016, Volume 38, Issue 3, pp. 504 - 517
Journal Article
IEEE Transactions on Automatic Control, ISSN 0018-9286, 07/2014, Volume 59, Issue 7, pp. 1765 - 1777
Journal Article
IEEE Transactions on Signal Processing, ISSN 1053-587X, 12/2016, Volume 64, Issue 23, pp. 6160 - 6173
The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data,... 
Analytical models | factor analysis | Laplace equations | Laplacian matrix learning | Signal processing algorithms | Signal processing | representation theory | Topology | Gaussian prior | Signal representation | Kernel | graph signal processing | BRAIN CONNECTIVITY | WAVELET | MODEL | VARIABLE SELECTION | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Algorithms | Kernel functions
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 12/2015, Volume 486, pp. 454 - 468
Let G be a simple graph with n vertices, m edges, maximum degree Δ, average degree d‾=2mn, clique number ω having Laplacian eigenvalues μ1,μ2,…,μn−1,μn=0. For... 
Zagreb index | Clique number | Laplacian energy | Average degree | Laplacian spectrum | 05C50 | MSC 05C30 | MATHEMATICS, APPLIED | PI-ELECTRON ENERGY | INVARIANT | SUM | THRESHOLD GRAPHS | MATHEMATICS | UPPER-BOUNDS | TREES | MOLECULAR-ORBITALS | SPECTRUM | INDEXES
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 2006, Volume 414, Issue 1, pp. 29 - 37
Let G be a graph with n vertices and m edges. Let λ 1, λ 2, … , λ n be the eigenvalues of the adjacency matrix of G, and let μ 1, μ 2, … , μ n be the... 
Energy (of graph) | Laplacian energy (of graph) | Laplacian graph spectrum | Graph spectrum | MATHEMATICS, APPLIED | PI-ELECTRON ENERGY | laplacian energy (of graph) | graph spectrum | laplacian graph spectrum | SPECTRUM | energy (of graph) | MINIMAL ENERGY | Universities and colleges
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2018, Volume 461, Issue 2, pp. 1299 - 1307
Let G be a simple graph with n vertices and let μ1≥μ2≥⋯≥μn=0 be the Laplacian eigenvalues of G. The k-th Laplacian spectral moment of G is defined to... 
Laplacian spectral moment | Erdős–Rényi random graph | Laplacian Estrada index | Random multipartite graph | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | ENERGY | SUM | POWERS | Erdos-Renyi random graph
Journal Article
IEEE Transactions on Circuits and Systems for Video Technology, ISSN 1051-8215, 07/2014, Volume 24, Issue 7, pp. 1088 - 1100
Journal Article
PLoS ONE, ISSN 1932-6203, 03/2015, Volume 10, Issue 3, p. e0123426
Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it... 
SMALLEST | ENERGY | NETWORKS | MULTIDISCIPLINARY SCIENCES | Models, Theoretical | Algorithms | Algebra | Lower bounds | Networks | Mathematical analysis | Linear algebra | Evolution | Graphs | Graph theory | Eigen values
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 02/2015, Volume 253, pp. 205 - 214
Let μ1⩾μ2⩾⋯⩾μn denote the Laplacian eigenvalues of a graph G with n vertices. The Laplacian-energy-like invariant, denoted by LEL(G)=∑i=1n-1μi, is a novel... 
Laplacian-energy-like invariant | Kirchhoff index | Laplacian values | Energy | Laplacian spectrum | Lattice | MATHEMATICS, APPLIED | GRAPHS
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 11/2019, Volume 581, pp. 336 - 353
Let G be a graph of order n, and let q1(G)≥q2(G)≥⋯≥qn(G) denote the signless Laplacian eigenvalues of G. Ashraf and Tayfeh-Rezaie (2014) [3] showed that... 
Signless Laplacian eigenvalue | Quotient matrix | Nordhaus–Gaddum type inequalities | Interlacing | MATHEMATICS | MATHEMATICS, APPLIED | SPREAD | Nordhaus-Gaddum type inequalities | 2ND LARGEST EIGENVALUE | Eigenvalues | Graphs
Journal Article
Fuzzy Sets and Systems, ISSN 0165-0114, 08/2019, Volume 368, pp. 119 - 136
Journal Article
Communications on Pure and Applied Mathematics, ISSN 0010-3640, 08/2012, Volume 65, Issue 8, pp. 1067 - 1144
We introduce vector diffusion maps (VDM), a new mathematical framework for organizing and analyzing massive high‐dimensional data sets, images, and shapes.... 
GRAPH | MATHEMATICS | CONSISTENCY | MATHEMATICS, APPLIED | NONLINEAR DIMENSIONALITY REDUCTION | MANIFOLDS | EIGENMAPS | RECONSTITUTION | REPRESENTATION THEORETIC PATTERNS
Journal Article