Academic literature on the topic 'Spectral graph theory'

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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
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Alrawayati, Hawa Ahmed, and Ümit Tokeşer. "Spectral Integral Variation of Graph Theory." Asian Journal of Mathematics and Computer Research 32, no. 2 (2025): 151–60. https://doi.org/10.56557/ajomcor/2025/v32i29173.

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Spectral integral variation in graph theory explores the interplay between the spectral properties of graphs and their topological and geometrical characteristics. This study focuses on the eigenvalues and eigenvectors of graph-related matrices, such as the adjacency matrix and the Laplacian matrix, and their implications for understanding graph structure, connectivity, and dynamics. By examining integral variations, we establish a framework for analyzing how spectral properties change under perturbations, such as edge weight modifications and graph transformations. This paper discusses the si
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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 indi
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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
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Hayat, Sakander, Asad Khan, and Mohammed J. F. Alenazi. "On Some Distance Spectral Characteristics of Trees." Axioms 13, no. 8 (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 eigenva
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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 (2011): 129–50. http://dx.doi.org/10.1016/j.acha.2010.04.005.

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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 (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 transfe
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Sason, Igal, Noam Krupnik, Suleiman Hamud, and Abraham Berman. "On Spectral Graph Determination." Mathematics 13, no. 4 (2025): 549. https://doi.org/10.3390/math13040549.

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The study of spectral graph determination is a fascinating area of research in spectral graph theory and algebraic combinatorics. This field focuses on examining the spectral characterization of various classes of graphs, developing methods to construct or distinguish cospectral nonisomorphic graphs, and analyzing the conditions under which a graph’s spectrum uniquely determines its structure. This paper presents an overview of both classical and recent advancements in these topics, along with newly obtained proofs of some existing results, which offer additional insights.
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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 (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
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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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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
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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.<br>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
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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 ma
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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 relate
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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<br>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,
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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 struc
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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
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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 d
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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
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Books on the topic "Spectral graph theory"

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

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

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

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

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

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Guattery, Stephen. Graph embedding techniques for bounding condition numbers of incomplete factor preconditioners. 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. 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-. Matematički institut SANU, 2009.

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Cvetković, Dragoš M. Selected topics on applications of graph spectra. Edited by Gutman Ivan 1947-. 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 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. 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. 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. 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. 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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Balakrishnan, R., and K. Ranganathan. "Spectral Properties of Graphs." In A Textbook of Graph Theory. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4529-6_11.

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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. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-50901-3_17.

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

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Rama, R. "Spectral Properties of Graphs." In Topics in Combinatorics and Graph Theory. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-74252-1_22.

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

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Sukumar, N. "Network Measures and Spectral Graph Theory." In SpringerBriefs in Materials. Springer Nature Switzerland, 2024. https://doi.org/10.1007/978-3-031-76290-1_3.

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Conference papers on the topic "Spectral graph theory"

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Sowjanya, M., K. M. Devendraiah, V. Kalpana, K. Venkata Ramana, Bramah Hazela, and Karthik Kumar Vaigandla. "Advanced Fake News and Hate Speech Detection Leveraging Spectral Graph Theory." In 2024 International Conference on Distributed Systems, Computer Networks and Cybersecurity (ICDSCNC). IEEE, 2024. https://doi.org/10.1109/icdscnc62492.2024.10939449.

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Bajpai, Chhavi, Manish Gaur, J. Roselin Suganthi, Vinayagam S, S. Kaliappan, and Manoj Senthil K. "Artificial Driving and Spectral Graph Theory for Automated Plant Leaf Disease Classification." In 2024 International Conference on Distributed Systems, Computer Networks and Cybersecurity (ICDSCNC). IEEE, 2024. https://doi.org/10.1109/icdscnc62492.2024.10939886.

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Ranieri, Andrea, Floriana Pichiorri, Elena Mongiardini, et al. "Spectral graph theory to investigate topological and dynamic properties of EEG-based brain networks: an application to post-stroke patients." In 2024 46th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). IEEE, 2024. https://doi.org/10.1109/embc53108.2024.10781512.

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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. Singidunum University, 2017. http://dx.doi.org/10.15308/sinteza-2017-182-185.

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Pena, Rodrigo, Xavier Bresson та Pierre Vandergheynst. "Source localization on graphs via ℓ1 recovery and spectral graph theory". У 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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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), 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), 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.], 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 networ
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