Relevant bibliographies by topics / Spectral graph theory

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Spectral graph theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 28 September 2024

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Journal articles on the topic "Spectral graph theory"

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Cvetkovic, Dragos. "Spectral recognition of graphs." Yugoslav Journal of Operations Research 22, no. 2 (2012): 145–61. http://dx.doi.org/10.2298/yjor120925025c.

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At some time, in the childhood of spectral graph theory, it was conjectured that non-isomorphic graphs have different spectra, i.e. that graphs are characterized by their spectra. Very quickly this conjecture was refuted and numerous examples and families of non-isomorphic graphs with the same spectrum (cospectral graphs) were found. Still some graphs are characterized by their spectra and several mathematical papers are devoted to this topic. In applications to computer sciences, spectral graph theory is considered as very strong. The benefit of using graph spectra in treating graphs is that eigenvalues and eigenvectors of several graph matrices can be quickly computed. Spectral graph parameters contain a lot of information on the graph structure (both global and local) including some information on graph parameters that, in general, are computed by exponential algorithms. Moreover, in some applications in data mining, graph spectra are used to encode graphs themselves. The Euclidean distance between the eigenvalue sequences of two graphs on the same number of vertices is called the spectral distance of graphs. Some other spectral distances (also based on various graph matrices) have been considered as well. Two graphs are considered as similar if their spectral distance is small. If two graphs are at zero distance, they are cospectral. In this sense, cospectral graphs are similar. Other spectrally based measures of similarity between networks (not necessarily having the same number of vertices) have been used in Internet topology analysis, and in other areas. The notion of spectral distance enables the design of various meta-heuristic (e.g., tabu search, variable neighbourhood search) algorithms for constructing graphs with a given spectrum (spectral graph reconstruction). Several spectrally based pattern recognition problems appear in many areas (e.g., image segmentation in computer vision, alignment of protein-protein interaction networks in bio-informatics, recognizing hard instances for combinatorial optimization problems such as the travelling salesman problem). We give a survey of such and other graph spectral recognition techniques used in computer sciences.
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Arsic, Branko, Dragos Cvetkovic, Slobodan Simic, and Milan Skaric. "Graph spectral techniques in computer sciences." Applicable Analysis and Discrete Mathematics 6, no. 1 (2012): 1–30. http://dx.doi.org/10.2298/aadm111223025a.

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We give a survey of graph spectral techniques used in computer sciences. The survey consists of a description of particular topics from the theory of graph spectra independently of the areas of Computer science in which they are used. We have described the applications of some important graph eigenvalues (spectral radius, algebraic connectivity, the least eigenvalue etc.), eigenvectors (principal eigenvector, Fiedler eigenvector and other), spectral reconstruction problems, spectra of random graphs, Hoffman polynomial, integral graphs etc. However, for each described spectral technique we indicate the fields in which it is used (e.g. in modelling and searching Internet, in computer vision, pattern recognition, data mining, multiprocessor systems, statistical databases, and in several other areas). We present some novel mathematical results (related to clustering and the Hoffman polynomial) as well.
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Hammond, David K., Pierre Vandergheynst, and Rémi Gribonval. "Wavelets on graphs via spectral graph theory." Applied and Computational Harmonic Analysis 30, no. 2 (March 2011): 129–50. http://dx.doi.org/10.1016/j.acha.2010.04.005.

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Hayat, Sakander, Asad Khan, and Mohammed J. F. Alenazi. "On Some Distance Spectral Characteristics of Trees." Axioms 13, no. 8 (July 23, 2024): 494. http://dx.doi.org/10.3390/axioms13080494.

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Graham and Pollack in 1971 presented applications of eigenvalues of the distance matrix in addressing problems in data communication systems. Spectral graph theory employs tools from linear algebra to retrieve the properties of a graph from the spectrum of graph-theoretic matrices. The study of graphs with “few eigenvalues” is a contemporary problem in spectral graph theory. This paper studies graphs with few distinct distance eigenvalues. After mentioning the classification of graphs with one and two distinct distance eigenvalues, we mainly focus on graphs with three distinct distance eigenvalues. Characterizing graphs with three distinct distance eigenvalues is “highly” non-trivial. In this paper, we classify all trees whose distance matrix has precisely three distinct eigenvalues. Our proof is different from earlier existing proof of the result as our proof is extendable to other similar families such as unicyclic and bicyclic graphs. The main tools which we employ include interlacing and equitable partitions. We also list all the connected graphs on ν ≤ 6 vertices and compute their distance spectra. Importantly, all these graphs on ν ≤ 6 vertices are determined from their distance spectra. We deliver a distance cospectral pair of order 7, thus making it a distance cospectral pair of the smallest order. This paper is concluded with some future directions.
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Cvetkovic, Dragos, and Slobodan Simic. "Towards a spectral theory of graphs based on the signless Laplacian, I." Publications de l'Institut Math?matique (Belgrade) 85, no. 99 (2009): 19–33. http://dx.doi.org/10.2298/pim0999019c.

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A spectral graph theory is a theory in which graphs are studied by means of eigenvalues of a matrix M which is in a prescribed way defined for any graph. This theory is called M-theory. We outline a spectral theory of graphs based on the signless Laplacians Q and compare it with other spectral theories, in particular with those based on the adjacency matrix A and the Laplacian L. The Q-theory can be composed using various connections to other theories: equivalency with A-theory and L-theory for regular graphs, or with L-theory for bipartite graphs, general analogies with A-theory and analogies with A-theory via line graphs and subdivision graphs. We present results on graph operations, inequalities for eigenvalues and reconstruction problems.
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Jin, Ming, Heng Chang, Wenwu Zhu, and Somayeh Sojoudi. "Power up! Robust Graph Convolutional Network via Graph Powering." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 9 (May 18, 2021): 8004–12. http://dx.doi.org/10.1609/aaai.v35i9.16976.

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Graph convolutional networks (GCNs) are powerful tools for graph-structured data. However, they have been recently shown to be vulnerable to topological attacks. To enhance adversarial robustness, we go beyond spectral graph theory to robust graph theory. By challenging the classical graph Laplacian, we propose a new convolution operator that is provably robust in the spectral domain and is incorporated in the GCN architecture to improve expressivity and interpretability. By extending the original graph to a sequence of graphs, we also propose a robust training paradigm that encourages transferability across graphs that span a range of spatial and spectral characteristics. The proposed approaches are demonstrated in extensive experiments to simultaneously improve performance in both benign and adversarial situations.
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Abdian, Ali Zeydi, and S. Morteza Mirafzal. "The spectral characterizations of the connected multicone graphs Kw ▽ LHS and Kw ▽ LGQ(3,9)." Discrete Mathematics, Algorithms and Applications 10, no. 02 (April 2018): 1850019. http://dx.doi.org/10.1142/s1793830918500192.

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In the past decades, graphs that are determined by their spectrum have received much more and more attention, since they have been applied to several fields, such as randomized algorithms, combinatorial optimization problems and machine learning. An important part of spectral graph theory is devoted to determining whether given graphs or classes of graphs are determined by their spectra or not. So, finding and introducing any class of graphs which are determined by their spectra can be an interesting and important problem. The main aim of this study is to characterize two classes of multicone graphs which are determined by their adjacency, Laplacian and signless Laplacian spectra. A multicone graph is defined to be the join of a clique and a regular graph. Let [Formula: see text] denote a complete graph on [Formula: see text] vertices. In the paper, we show that multicone graphs [Formula: see text] and [Formula: see text] are determined by both their adjacency spectra and their Laplacian spectra, where [Formula: see text] and [Formula: see text] denote the Local Higman–Sims graph and the Local [Formula: see text] graph, respectively. In addition, we prove that these multicone graphs are determined by their signless Laplacian spectra.
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Yu, Guidong, Tao Yu, Xiangwei Xia, and Huan Xu. "Spectral Sufficient Conditions on Pancyclic Graphs." Complexity 2021 (July 15, 2021): 1–8. http://dx.doi.org/10.1155/2021/3630245.

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A pancyclic graph of order n is a graph with cycles of all possible lengths from 3 to n . In fact, it is NP-complete that deciding whether a graph is pancyclic. Because the spectrum of graphs is convenient to be calculated, in this study, we try to use the spectral theory of graphs to study this problem and give some sufficient conditions for a graph to be pancyclic in terms of the spectral radius and the signless Laplacian spectral radius of the graph.
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Lurie, Jacob. "Review of Spectral Graph Theory." ACM SIGACT News 30, no. 2 (June 1999): 14–16. http://dx.doi.org/10.1145/568547.568553.

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Li, Dan, Guoping Wang, and Jixiang Meng. "On the distance signless Laplacian spectral radius of graphs and digraphs." Electronic Journal of Linear Algebra 32 (February 6, 2017): 438–46. http://dx.doi.org/10.13001/1081-3810.1982.

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Let \eta(G) denote the distance signless Laplacian spectral radius of a connected graph G. In this paper,bounds for the distance signless Laplacian spectral radius of connected graphs are given, and the extremal graph with the minimal distance signless Laplacian spectral radius among the graphs with given vertex connectivity and minimum degree is determined. Furthermore, the digraph that minimizes the distance signless Laplacian spectral radius with given vertex connectivity is characterized.
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Dissertations / Theses on the topic "Spectral graph theory"

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Peng, Richard. "Algorithm Design Using Spectral Graph Theory." Research Showcase @ CMU, 2013. http://repository.cmu.edu/dissertations/277.

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Spectral graph theory is the interplay between linear algebra and combinatorial graph theory. Laplace’s equation and its discrete form, the Laplacian matrix, appear ubiquitously in mathematical physics. Due to the recent discovery of very fast solvers for these equations, they are also becoming increasingly useful in combinatorial optimization, computer vision, computer graphics, and machine learning. In this thesis, we develop highly efficient and parallelizable algorithms for solving linear systems involving graph Laplacian matrices. These solvers can also be extended to symmetric diagonally dominant matrices and M-matrices, both of which are closely related to graph Laplacians. Our algorithms build upon two decades of progress on combinatorial preconditioning, which connects numerical and combinatorial algorithms through spectral graph theory. They in turn rely on tools from numerical analysis, metric embeddings, and random matrix theory. We give two solver algorithms that take diametrically opposite approaches. The first is motivated by combinatorial algorithms, and aims to gradually break the problem into several smaller ones. It represents major simplifications over previous solver constructions, and has theoretical running time comparable to sorting. The second is motivated by numerical analysis, and aims to rapidly improve the algebraic connectivity of the graph. It is the first highly efficient solver for Laplacian linear systems that parallelizes almost completely. Our results improve the performances of applications of fast linear system solvers ranging from scientific computing to algorithmic graph theory. We also show that these solvers can be used to address broad classes of image processing tasks, and give some preliminary experimental results.
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Florkowski, Stanley F. "Spectral graph theory of the Hypercube." Thesis, Monterey, Calif. : Naval Postgraduate School, 2008. http://edocs.nps.edu/npspubs/scholarly/theses/2008/Dec/08Dec%5FFlorkowski.pdf.

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Thesis (M.S. in Applied Mathematics)--Naval Postgraduate School, December 2008.
Thesis Advisor(s): Rasmussen, Craig W. "December 2008." Description based on title screen as viewed on January 29, 2009. Includes bibliographical references (p. 51-52). Also available in print.
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Huang, Peng. "Spectral radius and signless Laplacian spectral radius of k-connected graphs /Huang Peng." HKBU Institutional Repository, 2016. https://repository.hkbu.edu.hk/etd_oa/373.

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The adjacency matrix of a graph is a (0, 1)-matrix indexed by the vertex set of the graph. And the signless Laplacian matrix of a graph is the sum of its adjacency matrix and its diagonal matrix of vertex degrees. The eigenvalues and the signless Laplacian eigenvalues of a graph are the eigenvalues of the adjacency matrix and the signless Laplacian matrix, respectively. These two matrices of a graph have been studied for several decades since they have been applied to many research field, such as computer science, communication network, information science and so on. In this thesis, we study k-connected graphs and focus on their spectral radius and signless Laplacian spectral radius. Firstly, we determine the graphs with maximum spectral radius among all k-connected graphs of fixed order with given diameter. As we know, when a graph is regular, its spectral radius and signless Laplacian spectral radius can easily be found. We obtain an upper bound on the signless Laplacian spectral radius of k-connected irregular graphs. Finally, we give some other results mainly related to the signless Laplacian matrix.
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Rittenhouse, Michelle L. "Properties and Recent Applications in Spectral Graph Theory." VCU Scholars Compass, 2008. http://scholarscompass.vcu.edu/etd/1126.

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There are numerous applications of mathematics, specifically spectral graph theory, within the sciences and many other fields. This paper is an exploration of recent applications of spectral graph theory, including the fields of chemistry, biology, and graph coloring. Topics such as the isomers of alkanes, the importance of eigenvalues in protein structures, and the aid that the spectra of a graph provides when coloring a graph are covered, as well as others.The key definitions and properties of graph theory are introduced. Important aspects of graphs, such as the walks and the adjacency matrix are explored. In addition, bipartite graphs are discussed along with properties that apply strictly to bipartite graphs. The main focus is on the characteristic polynomial and the eigenvalues that it produces, because most of the applications involve specific eigenvalues. For example, if isomers are organized according to their eigenvalues, a pattern comes to light. There is a parallel between the size of the eigenvalue (in comparison to the other eigenvalues) and the maximum degree of the graph. The maximum degree of the graph tells us the most carbon atoms attached to any given carbon atom within the structure. The Laplacian matrix and many of its properties are discussed at length, including the classical Matrix Tree Theorem and Cayley's Tree Theorem. Also, an alternative approach to defining the Laplacian is explored and compared to the traditional Laplacian.
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Morisi, Rita. "Graph–based techniques and spectral graph theory in control and machine learning." Thesis, IMT Alti Studi Lucca, 2016. http://e-theses.imtlucca.it/188/1/Morisi_phdthesis.pdf.

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Graphs are powerful data structure for representing objects and their relationships. They are extremely useful in the study of dynamical systems, evaluating how different agents interact among each other and behave. An example is represented by the consensus problem where a graph models a set of agents that locally interact and exchange their opinions with the aim of reaching a common opinion (consensus state). At the same time, many learning techniques rely on graphs exploiting their potentialities in modeling the relationships between data and determining additional features related to the data similarities. To study both the consensus problem and specific machine learning applications based on graphs, the study of the spectral properties of graphs reveals fundamental. In the consensus problem, the convergence rate to the consensus state strictly depends on the spectral properties of the transition probability matrix associated to the agents network. Whereas graphs and their spectral properties are fundamental in determining learning algorithms able to capture the structure of a dataset. We propose a theoretical and numerical study of the spectral properties of a network of agents that interact with the aim of increasing the rate of convergence to the consensus state keeping as sparse as possible the graph involved. Experimental results demonstrate the capability of the proposed approach in reaching the consensus state faster than a classical approach. We then investigate the potentialities of graphs when applied in classification problems. The results achieved highlight the importance of graphs and their spectral properties handling with both semi–supervised and supervised learning problems.
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Johnson, Jamie L. "Software defined network monitoring scheme using spectral graph theory and phantom nodes." Thesis, Monterey, California: Naval Postgraduate School, 2014. http://hdl.handle.net/10945/43933.

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Approved for public release; distribution is unlimited
In this thesis, we propose a new software defined network monitoring scheme that provides the controller with a method to determine network states for the purpose of updating flow rules for network control and management. Network centrality and nodal influence metrics derived from the dual basis concept of the graph theory are used to monitor changes in a network. The proposed scheme uses a phantom node and the concept of a reference node to determine changes in these metrics in order to identify disconnected, congested, underutilized, and attacked nodes. The phantom node establishes a congestion threshold in the dual basis that is used to determine changes in node health and capacity due to network traffic. Multiple phantom nodes are used to produce multiple congestion thresholds for network monitoring. A congestion estimation method is proposed to estimate a node’s capacity used when it crosses the congestion threshold. Simulations are used to validate the concept of reference node, identification of node disconnections, congestion, and attacks, and the congestion estimation method.
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Lucas, Claire. "Trois essais sur les relations entre les invariants structuraux des graphes et le spectre du Laplacien sans signe." Phd thesis, Ecole Polytechnique X, 2013. http://pastel.archives-ouvertes.fr/pastel-00956183.

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Le spectre du Laplacien sans signe a fait l'objet de beaucoup d'attention dans la communauté scientifique ces dernières années. La principale raison est l'intuition, basée sur une étude des petits graphes et sur des propriétés valides pour des graphes de toutes tailles, que plus de graphes sont déterminés par le spectre de cette matrice que par celui de la matrice d'adjacence et du Laplacien. Les travaux présentés dans cette thèse ont apporté des éléments nouveaux sur les informations contenues dans le spectre cette matrice. D'une part, on y présente des relations entre les invariants de structure et une valeur propre du Laplacien sans signe. D'autre part, on présente des familles de graphes extrêmes pour deux de ses valeurs propres, avec et sans contraintes additionnelles sur la forme de graphe. Il se trouve que ceux-ci sont très similaires à ceux obtenus dans les mêmes conditions avec les valeurs propres de la matrice d'adjacence. Cela aboutit à la définition de familles de graphes pour lesquelles, le spectre du Laplacien sans signe ou une de ses valeurs propres, le nombre de sommets et un invariant de structure suffisent à déterminer le graphe. Ces résultats, par leur similitude avec ceux de la littérature viennent confirmer l'idée que le Laplacien sans signe détermine probablement aussi bien les graphes que la matrice d'adjacence.
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Ghenciu, Eugen Andrei. "Dimension spectrum and graph directed Markov systems." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5226/.

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In this dissertation we study graph directed Markov systems (GDMS) and limit sets associated with these systems. Given a GDMS S, by the Hausdorff dimension spectrum of S we mean the set of all positive real numbers which are the Hausdorff dimension of the limit set generated by a subsystem of S. We say that S has full Hausdorff dimension spectrum (full HD spectrum), if the dimension spectrum is the interval [0, h], where h is the Hausdorff dimension of the limit set of S. We give necessary conditions for a finitely primitive conformal GDMS to have full HD spectrum. A GDMS is said to be regular if the Hausdorff dimension of its limit set is also the zero of the topological pressure function. We show that every number in the Hausdorff dimension spectrum is the Hausdorff dimension of a regular subsystem. In the particular case of a conformal iterated function system we show that the Hausdorff dimension spectrum is compact. We introduce several new systems: the nearest integer GDMS, the Gauss-like continued fraction system, and the Renyi-like continued fraction system. We prove that these systems have full HD spectrum. A special attention is given to the backward continued fraction system that we introduce and we prove that it has full HD spectrum. This system turns out to be a parabolic iterated function system and this makes the analysis more involved. Several examples have been constructed in the past of systems not having full HD spectrum. We give an example of such a system whose limit set has positive Lebesgue measure.
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Behjat, Hamid. "Statistical Parametric Mapping of fMRI data using Spectral Graph Wavelets." Thesis, Linköpings universitet, Medicinsk informatik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-81143.

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In typical statistical parametric mapping (SPM) of fMRI data, the functional data are pre-smoothed using a Gaussian kernel to reduce noise at the cost of losing spatial specificity. Wavelet approaches have been incorporated in such analysis by enabling an efficient representation of the underlying brain activity through spatial transformation of the original, un-smoothed data; a successful framework is the wavelet-based statistical parametric mapping (WSPM) which enables integrated wavelet processing and spatial statistical testing. However, in using the conventional wavelets, the functional data are considered to lie on a regular Euclidean space, which is far from reality, since the underlying signal lies within the complex, non rectangular domain of the cerebral cortex. Thus, using wavelets that function on more complex domains such as a graph holds promise. The aim of the current project has been to integrate a recently developed spectral graph wavelet transform as an advanced transformation for fMRI brain data into the WSPM framework. We introduce the design of suitable weighted and un-weighted graphs which are defined based on the convoluted structure of the cerebral cortex. An optimal design of spatially localized spectral graph wavelet frames suitable for the designed large scale graphs is introduced. We have evaluated the proposed graph approach for fMRI analysis on both simulated as well as real data. The results show a superior performance in detecting fine structured, spatially localized activation maps compared to the use of conventional wavelets, as well as normal SPM. The approach is implemented in an SPM compatible manner, and is included as an extension to the WSPM toolbox for SPM.
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Witt, Walter G. "Quantifying the Structure of Misfolded Proteins Using Graph Theory." Digital Commons @ East Tennessee State University, 2017. https://dc.etsu.edu/etd/3244.

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The structure of a protein molecule is highly correlated to its function. Some diseases such as cystic fibrosis are the result of a change in the structure of a protein so that this change interferes or inhibits its function. Often these changes in structure are caused by a misfolding of the protein molecule. To assist computational biologists, there is a database of proteins together with their misfolded versions, called decoys, that can be used to test the accuracy of protein structure prediction algorithms. In our work we use a nested graph model to quantify a selected set of proteins that have two single misfold decoys. The graph theoretic model used is a three tiered nested graph. Measures based on the vertex weights are calculated and we compare the quantification of the proteins with their decoys. Our method is able to separate the misfolded proteins from the correctly folded proteins.
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Books on the topic "Spectral graph theory"

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Cvetković, Dragoš M. Eigenspaces of graphs. Cambridge: Cambridge University Press, 1997.

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Cvetković, Dragoš M. Eigenspaces of graphs. Cambridge: Cambridge University Press, 2008.

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Cvetković, Dragoš M. Spectra of graphs: Theory and applications. 3rd ed. Heidelberg: Johann Ambrosius Barth, 1995.

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H, Haemers Willem, and SpringerLink (Online service), eds. Spectra of Graphs. New York, NY: Andries E. Brouwer and Willem H. Haemers, 2012.

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Verdière, Yves Colin de. Spectres de graphes. Paris: Société mathématique de France, 1998.

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Guattery, Stephen. Graph embedding techniques for bounding condition numbers of incomplete factor preconditioners. Hampton, Va: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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Center, Langley Research, ed. Graph embedding techniques for bounding condition numbers of incomplete factor preconditioners. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1997.

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Cvetković, Dragoš M. Applications of graph spectra. Edited by Gutman Ivan 1947-. Beograd: Matematički institut SANU, 2009.

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Cvetković, Dragoš M. Selected topics on applications of graph spectra. Edited by Gutman Ivan 1947-. Beograd: Matematički institut SANU, 2011.

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Peter, Rowlinson, Simić S. (Slobodan), and London Mathematical Society, eds. An introduction to the theory of graph spectra. Cambridge: Cambridge University Press, 2010.

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Book chapters on the topic "Spectral graph theory"

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Jeribi, Aref. "Spectral Graph Theory." In Spectral Theory and Applications of Linear Operators and Block Operator Matrices, 413–39. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-17566-9_12.

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Yadav, Santosh Kumar. "Spectral Properties of Graphs." In Advanced Graph Theory, 243–52. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-22562-8_9.

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Kurasov, Pavel. "Standard Laplacians and Secular Polynomials." In Operator Theory: Advances and Applications, 123–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 2023. http://dx.doi.org/10.1007/978-3-662-67872-5_6.

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AbstractIn this chapter we start systematic studies of spectral properties of graph Laplacians—standard Laplace operators on metric graphs. Our main interest will be families of metric graphs having the same topological structure. Metric graphs from such a family correspond to the same discrete graph but the lengths of the edges may be different. Common spectral properties of such families (and hence of all metric graphs) are best described by certain multivariate low degree polynomials.
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Kurasov, Pavel. "The Trace Formula." In Operator Theory: Advances and Applications, 179–208. Berlin, Heidelberg: Springer Berlin Heidelberg, 2023. http://dx.doi.org/10.1007/978-3-662-67872-5_8.

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AbstractThis chapter is devoted to the trace formula connecting the spectrum of a finite compact metric graph with the set of closed paths on it. In other words this formula establishes a relation between spectral and geometric/topologic properties of metric graphs.
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Crawford, Brian, Ralucca Gera, Jeffrey House, Thomas Knuth, and Ryan Miller. "Graph Structure Similarity using Spectral Graph Theory." In Studies in Computational Intelligence, 209–21. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-50901-3_17.

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Balakrishnan, R., and K. Ranganathan. "Spectral Properties of Graphs." In A Textbook of Graph Theory, 241–73. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4529-6_11.

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Hoppen, Carlos, David P. Jacobs, and Vilmar Trevisan. "Domination and Spectral Graph Theory." In Developments in Mathematics, 245–72. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-58892-2_9.

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Kurasov, Pavel. "Elementary Spectral Properties of Quantum Graphs." In Operator Theory: Advances and Applications, 65–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 2023. http://dx.doi.org/10.1007/978-3-662-67872-5_4.

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Sin’ya, Ryoma. "Graph Spectral Properties of Deterministic Finite Automata." In Developments in Language Theory, 76–83. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09698-8_8.

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Dai, Qionghai, and Yue Gao. "Neural Networks on Hypergraph." In Artificial Intelligence: Foundations, Theory, and Algorithms, 121–43. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-0185-2_7.

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AbstractWith the development of deep learning on high-order correlations, hypergraph neural networks have received much attention in recent years. Generally, the neural networks on hypergraph can be divided into two categories, including the spectral-based methods and the spatial-based methods. For the spectral-based methods, the convolution operation is formulated in the spectral domain of graph, and we introduce the typical spectral-based methods, including hypergraph neural networks (HGNN), hypergraph convolution with attention (Hyper-Atten), and hyperbolic hypergraph neural network (HHGNN), which extend hypergraph computation to hyperbolic spaces beyond the Euclidean space. For the spatial-based methods, the convolution operation is defined in groups of spatially close vertices. We then present spatial-based hypergraph neural networks of the general hypergraph neural networks (HGNN+) and the dynamic hypergraph neural networks (DHGNN). Additionally, there are several convolution methods that attempt to reduce the hypergraph structure to the graph structure, so that the existing graph convolution methods can be directly deployed. Lastly, we analyze the association and comparison between hypergraph and graph in the two areas described above (spectral-based, spatial-based), further demonstrating the ability and advantages of hypergraph on constructing and computing higher-order correlations in the data.
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Conference papers on the topic "Spectral graph theory"

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Oliveira, Daniel, Carlos Magno Abreu, Eduardo Ogasawara, Eduardo Bezerra, and Leonardo De Lima. "A Science Gateway to Support Research in Spectral Graph Theory." In XXXIV Simpósio Brasileiro de Banco de Dados. Sociedade Brasileira de Computação - SBC, 2019. http://dx.doi.org/10.5753/sbbd.2019.8826.

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Describing classes of graphs that optimize a function of the eigenvalues subject to some constraints is one of the topics addressed by Spectral Graph Theory (SGT). In this paper, we propose RioGraphX, a science gateway developed on top of Apache Spark, which aims to obtain all graphs that optimize a given mathematical function of the eigenvalues of a graph. Initial experiments involving small graphs have pointed out optimal graphs in a reasonable computational time, and also have shown that leveraging parallel processing is a promising approach to handle larger graphs.
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Torres, Alvaro, and George Anders. "Spectral Graph Theory and Network Dependability." In 2009 Fourth International Conference on Dependability of Computer Systems. IEEE, 2009. http://dx.doi.org/10.1109/depcos-relcomex.2009.52.

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Spielman, Daniel A. "Spectral Graph Theory and its Applications." In 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07). IEEE, 2007. http://dx.doi.org/10.1109/focs.2007.56.

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Spielman, Daniel A. "Spectral Graph Theory and its Applications." In 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07). IEEE, 2007. http://dx.doi.org/10.1109/focs.2007.4389477.

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Chaparro-Vargas, Ramiro, Beena Ahmed, Thomas Penzel, and Dean Cvetkovic. "Characterising insomnia: A graph spectral theory approach." In 2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). IEEE, 2015. http://dx.doi.org/10.1109/embc.2015.7318375.

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Jovanović, Nenad, Zoran Jovanović, and Aleksandar Jevremović. "Complex Networks Analysis by Spectral Graph Theory." In Sinteza 2017. Belgrade, Serbia: Singidunum University, 2017. http://dx.doi.org/10.15308/sinteza-2017-182-185.

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Pena, Rodrigo, Xavier Bresson, and Pierre Vandergheynst. "Source localization on graphs via ℓ1 recovery and spectral graph theory." In 2016 IEEE 12th Image, Video, and Multidimensional Signal Processing Workshop (IVMSP). IEEE, 2016. http://dx.doi.org/10.1109/ivmspw.2016.7528230.

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Ouahada, Khmaies, and Hendrik C. Ferreira. "A graph theoretic approach for spectral null codes." In 2009 IEEE Information Theory Workshop. IEEE, 2009. http://dx.doi.org/10.1109/itw.2009.5351185.

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Miller, Gary L. "Solving large optimization problems using spectral graph theory." In the 45th annual ACM symposium. New York, New York, USA: ACM Press, 2013. http://dx.doi.org/10.1145/2488608.2488689.

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Edstrom, F., and L. Soder. "On spectral graph theory in power system restoration." In 2011 2nd IEEE PES International Conference and Exhibition on "Innovative Smart Grid Technologies" (ISGT Europe). IEEE, 2011. http://dx.doi.org/10.1109/isgteurope.2011.6162615.

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Reports on the topic "Spectral graph theory"

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Sweeney, Matthew, and Emily Shinkle. Understanding Discrete Fracture Networks Through Spectral Graph Theory. Office of Scientific and Technical Information (OSTI), August 2021. http://dx.doi.org/10.2172/1812641.

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Sweeney, Matthew, and Emily Shinkle. Understanding Discrete Fracture Networks Through Spectral Graph Theory. Office of Scientific and Technical Information (OSTI), August 2021. http://dx.doi.org/10.2172/1812622.

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Soloviev, Vladimir, Victoria Solovieva, Anna Tuliakova, Alexey Hostryk, and Lukáš Pichl. Complex networks theory and precursors of financial crashes. [б. в.], October 2020. http://dx.doi.org/10.31812/123456789/4119.

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Based on the network paradigm of complexity in the work, a systematic analysis of the dynamics of the largest stock markets in the world and cryptocurrency market has been carried out. According to the algorithms of the visibility graph and recurrence plot, the daily values of stock and crypto indices are converted into a networks and multiplex networks, the spectral and topological properties of which are sensitive to the critical and crisis phenomena of the studied complex systems. This work is the first to investigate the network properties of the crypto index CCI30 and the multiplex network of key cryptocurrencies. It is shown that some of the spectral and topological characteristics can serve as measures of the complexity of the stock and crypto market, and their specific behaviour in the pre-crisis period is used as indicators- precursors of critical phenomena.
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