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Topic: Spectral graph theory

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	Spectral graph theory - Wikipedia, the free encyclopedia
		In mathematics, spectral graph theory is the study of properties of a graph in relationship to the characteristic polynomials, eigenvalues and eigenvectors of its adjacency matrix or Laplace matrix.
		Isospectral graphs need not be isomorphic, but isomorphic graphs are always isospectral, because the characteristic polynomial is a topological invariant of the graph.
		The study of the topological invariants of the Cayley graph is known as geometric group theory.
	en.wikipedia.org /wiki/Spectral_graph_theory (277 words)

	Encyclopedia: Graph theory (Site not responding. Last check: 2007-10-23)
		Algebraic graph theory is a branch of mathematics.
		In mathematics topological graph theory is a branch of graph theory.
		Extremal graph theory is a branch of mathematics.
	www.nationmaster.com /encyclopedia/Graph-theory (3471 words)

	Biadjacency matrix - Wikipedia, the free encyclopedia
		In the special case of a finite, undirected simple bipartite graph, the biadjacency matrix is a (0,1)-matrix.
		The relationship between a bipartite graph and its biadjacency matrix is studied in spectral graph theory.
		The adjacency matrix A for a bipartite graph with a biadjacency matrix B is given by
	en.wikipedia.org /wiki/Biadjacency_matrix (120 words)

	Spectral graph theory -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-23)
		An (additional info and facts about undirected graph) undirected graph has a (additional info and facts about symmetric) symmetric adjacency matrix and therefore has real eigenvalues and a complete set of (additional info and facts about orthonormal) orthonormal eigenvectors.
		Two graphs are said to be (additional info and facts about isospectral) isospectral if the adjacency matrices of the graphs have the same eigenvalues.
		The study of the topological invariants of the (additional info and facts about Cayley graph) Cayley graph is known as (additional info and facts about geometric group theory) geometric group theory.
	www.absoluteastronomy.com /encyclopedia/s/sp/spectral_graph_theory.htm (333 words)

	Spectral Graph Analysis (Site not responding. Last check: 2007-10-23)
		Each RNA graph has a Laplacian matrix representation and a corresponding eigenvalue spectrum (see Graph Isomorphism); the number of eigenvalues is equal to the rank of the matrix.
		The eigenvalues are related to the connectivity pattern (or topology) of the RNA graph.
		A large second eigenvalue indicates a compact graph, whereas a small eigenvalue implies an elongated topology.
	monod.biomath.nyu.edu /rna/tutorials/spectral_analysis.html (124 words)

	Expander graph - TheBestLinks.com - Cryptography, Combinatorics, Computer science, Graph theory, ... (Site not responding. Last check: 2007-10-23)
		In combinatorics, an expander graph is in rough terms a sparse graph with high vertex or edge expansion, or in other words highly connected.
		The expansion of a graph is related to the graph spectrum, studied in spectral graph theory.
		Ramanujan graphs are class of d-regular expander graphs, with explicit constructions, that achieve the largest gap between the first and second eigenvalues of the adjacency matrix.
	www.thebestlinks.com /Expander_graph.html (283 words)

	Graph Theory Books (Site not responding. Last check: 2007-10-23)
		The Foundations of Topological Graph Theory by Bonnington.CP and Little.CHC Springer Verlag 1996
		Distance-Regular Graphs by Brouwer.AE, A.M. Cohen, and A. Neumaier Springer-Verlag 1980
		Graphs: Theory and Algorithms by K. Thulasiraman and M.N.S. Swamy John Wiley and Sons 1992
	www1.cs.columbia.edu /~sanders/graphtheory/writings/books.html (376 words)

	Theory People
		The rich contribution of the group to the theory community is a witness to this fact.
		The theory group and those interested in theory topics meet once in a week for the STAR seminar (and for pizza of course), in which we present our own work or discuss recent interesting results in the area.
		Her main research interests lie in spectral graph theory and extremal graph theory.
	www.cse.ucsd.edu /groups/theory/people.html (420 words)

	Directory - Science: Math: Combinatorics: Graph Theory
		Graph Theory, as a branch of Combinatorics, MSC classification 05Cxx.
		A Constructive Approach to Graph Theory · cached · Notes on a semiotic approach to constructing isomorphism invariants of graphs by John-Tagore Tevet.
		Spectral Graph Theory · cached · People, publications, research topics, open problems, events and resources.
	www.incywincy.com /default?p=93022 (413 words)

	Spectral Clustering, ICML 2004 Tutorial by Chris Ding (Site not responding. Last check: 2007-10-23)
		At the core of spectral clustering is the Laplacian of the graph adjacency (pairwise similarity) matrix, evolved from spectral graph partitioning.
		The widely used K-means clustering is shown recently (Zha,et al 2001; Ding & He, 2003) to be directly related to spectral method: (a) the solution for cluster membership indicators are given by principal components, eigenvectors of the inner-product kernel (Gram) matrix; (b) PCA subspace is identical to the subspace spanned by K cluster centroids.
		A unifying theorem for spectral embedding and clustering.
	crd.lbl.gov /~cding/Spectral (771 words)

	Algebraic Graph Theory - Computing Science and Mathematics, University of Stirling
		The context for work in these areas is the relationship between the structure of a network graph and its algebraic invariants, which include the eigenvalues of an adjacency matrix.
		Several graphs can be characterised as maximal graphs with a prescribed star complement for a prescribed eigenvalue.
		A workshop on Algebraic Graph Theory at the International Centre for Mathematical Sciences, Edinburgh in July 1993.
	www.cs.stir.ac.uk /research/groups/alg-graph.html (423 words)

	Enlaces : Science : Math : Combinatorics : Graph_Theory :: 100cia.com (Site not responding. Last check: 2007-10-23)
		A Constructive Approach to Graph Theory - Notes on a semiotic approach to constructing isomorphism invariants of graphs by John-Tagore Tevet..
		Getgrats: General Theory of Graph Transformation Systems - A research network funded by the European Commission..
		Spectral Graph Theory - People, publications, research topics, open problems, events and resources..
	www.100cia.com /recursos/enlaces/Science/Math/Combinatorics/Graph_Theory (461 words)

	[No title] (Site not responding. Last check: 2007-10-23)
		The study of this question is the province of "spectral graph theory," and it makes interesting, beautiful, and useful connections between linear algebra and graph theory.
		I will survey some basic results in spectral graph theory and discuss the relationship between the spectrum of a graph, expansion properties, and random walks on a graph.
		I'll give some applications of spectral partitioning and sketch a result due to Spielman and Teng that shows "spectral partitioning works" for the case of planar graphs.
	www.cs.berkeley.edu /~dmolnar/spectral.html (124 words)

	[No title] (Site not responding. Last check: 2007-10-23)
		Spectral-graph theory allows graphs to be described in a compact form due to the fact that the set of leading eigenvalues and eigenvectors provide an embedding of the nodes in the graph into a k-dimensional subspace.
		Having reviewed existing methods, I will illustrate how graph-spectral theory and the apparatus of statistical inference can be used to develop algorithms for performing segmentation and grouping and graph matching.
		As a result, the graph edit distance can be computed finding the sequence of string edit operations, which minimise the cost of a path traversing the edit lattice.
	www.dcs.qmw.ac.uk /research/vision/seminars/kelly.txt (550 words)

	Spectral Graph Algorithms (Site not responding. Last check: 2007-10-23)
		Of all the deep connections between combinatorics and linear algebra, those in the field known as spectral graph theory are among the most mysterious.
		I have used eigenvectors of the Laplacian matrix in several different application domains including partitioning graphs, organizing databases and assembling gene fragments.
		An Improved Spectral Graph Partitioning Algorithm for Mapping Parallel Computations, Bruce Hendrickson and Robert Leland, SIAM J. Sci.
	www.cs.sandia.gov /~bahendr/spectral.html (161 words)

	Spectral Graph Theory (Site not responding. Last check: 2007-10-23)
		Many important examples of landscapes in physics and combinatorial optimization, which are widely used as model landscapes in simulations of molecular evolution and adaptation, are ``elementary'', i.e., they are (up to an additive constant) eigenfunctions of a graph Laplacian.
		The underlying graph itself is introduced in a natural way by a move set (mutation operator, search strategy) on the set of possible configurations or genes.
		The correlation functions are in turn uniquely determined by the geometry of the underlying configuration space and the nearest neighbor correlation of the elementary landscape.
	non.fiction.org /~await/alife/talks/maley/nov11-96.html (415 words)

	Algebraic Graph Theory (Site not responding. Last check: 2007-10-23)
		Book Description: Algebraic graph theory is a fascinating subject concerned with the interplay between algebra and graph theory.
		This book is primarily aimed at graduate students and researchers in graph theory, combinatorics, or discrete mathematics in general.
		However, all the necessary graph theory is developed from scratch, so the only pre-requisite for reading it is a first course in linear algebra and a small amount of elementary group theory.
	isbn.nu /0387952411 (628 words)

	Mark Goldberg's Graph Theory Page (Site not responding. Last check: 2007-10-23)
		Graph Tutorial interactive elementary introduction to graph theory
		Combinatorics and Graph Theory group in de Catalunya: Large Interconnection Nets; Routing; Tables
		Spectral Graph Theory Polymer structure prediction
	www.cs.rpi.edu /~goldberg/graph-theory (182 words)

	An Improved Spectral Graph Partitioning Algorithm for Mapping Parallel Computations - Hendrickson, Leland ... (Site not responding. Last check: 2007-10-23)
		We present a new domain mapping algorithm that extends recent work in which ideas from spectral graph theory have been applied to this problem.
		Our generalization of spectral graph bisection involves a novel use of multiple eigenvectors to allow for division of a computation into four or eight parts at each stage of a...
		The graph only includes citing articles where the year of publication is known.
	citeseer.ist.psu.edu /hendrickson95improved.html (599 words)

	Graphs: Theory - Algorithms - Complexity (Site not responding. Last check: 2007-10-23)
		Groups and Graphs: a software package for graphs, digraphs, combinatorial designs, and their automorphism groups, by B.
		Scheinerman, E.R., Ullman, D.H.: Fractional graph theory: a rational approach to the theory of graphs, John Wiley and Sons, New York, 1997.
		Graph connections -- relationships between graph theory and other areas of mathematics, Eds.
	people.freenet.de /Emden-Weinert/graphs.html (1244 words)

	Jacobs School Faculty Biography
		She is an authority on spectral-graph theory, extremal graphs, graph labeling, graph decompositions, random graphs, graph algorithms (all useful for visualizing and modeling networks), and parallel structures.
		A related matter is how accurately distance values, such as the average and maximum "hops" a data packet travels to destination, can be predicted using relatively few parameters.
		She is the author of two books -- "Erdös on Graphs" and "Spectral Graph Theory" - and is Co-Editor-in-Chief of Advances in Applied Mathematics.
	www.jacobsschool.ucsd.edu /FacBios/findprofile.pl?fmp_recid=107 (331 words)

	Mathematics Publications- Computing Science and Mathematics, University of Stirling (Site not responding. Last check: 2007-10-23)
		FRANCIS K. BELL and S. Simic, On graphs whose star complement for -2 is a path or a cycle, Linear Algebra and Its Applications, 377, pages 249-265, 2004.
		Beineke and R. Wilson, Topics in Algebraic Graph Theory, Encyclopedia of Mathematics and its applications Vol.102, Cambridge University Press, ISBN 0521 80197 4.
		Graphs with least eigenvalue -2: The star complement technique, Journal of Algebraic Combinatorics, 14, 5-16, 2001.
	www.cs.stir.ac.uk /research/publications/mathspubs (2128 words)

	Spectral Graph Theory, a book by Fan Chung (Site not responding. Last check: 2007-10-23)
		The stories will be told --- how the spectrum reveals fundamental properties of a graph, how spectral graph theory links the discrete universe to the continuous one through geometric, analytic and algebraic techniques, and how, through eigenvalues, theory and applications in communications and computer science come together in symbiotic harmony.
		Since spectral graph theory has been evolving very rapidly, the above goals can only be partially fulfilled here.
		Chapter 1 : Eigenvalues and the Laplacian of a graph
	math.ucsd.edu /~fan/outline.html (167 words)

	On Some Extremal Problems In Graph Theory - Jakobson, Rivin (ResearchIndex) (Site not responding. Last check: 2007-10-23)
		In this paper we are concerned with various graph invariants (girth, diameter, expansion constants, eigenvalues of the Laplacian, tree number) and their analogs for weighted graphs -- weighing the graph changes a combinatorial problem to one in analysis.
		We study both weighted and unweighted graphs which are extremal for these invariants.
		In the unweighted case we concentrate on finding extrema among all (usually) regular graphs with the same number of vertices; we also study the...
	citeseer.ist.psu.edu /jakobson98some.html (887 words)

	Theory of Spectral Graph Layout
		Typically, given edge weights, coordinates are desired for graph vertices such that some distance measure or cost function is minimized.
		The alternative is to sacrifice accuracy via some suboptimal approximate solution to the NP-hard problem such as simulated annealing, genetic search, or Kernighan-Lin-type directed-exchange schemes.
		This paper is about laying out graphs by minimizing the weighted sum of squares of mutual distances, constrained not to vanish always.
	research.microsoft.com /research/pubs/view.aspx?tr_id=86 (212 words)

	A Spectral Analysis of the Internet Topology - Vukadinovic, Huang, Erlebach (ResearchIndex) (Site not responding. Last check: 2007-10-23)
		Among techniques in spectral graph theory, we find the normalized Laplacian spectrum (nls) of AS graphs 1) unique in spite of the explosive growth of the Internet and 2) distinctive in setting AS graphs apart from synthetic ones.
		These properties suggest that nls is an excellent candidate as a concise fingerprint of Internet-like graphs.
		13 The Laplacian spectrum of a graph (context) - Grone, Merris et al.
	citeseer.ist.psu.edu /vukadinovic01spectral.html (495 words)

	Fan Chung (Site not responding. Last check: 2007-10-23)
		Fan Rong K Chung Graham (born 1949, known professionally as Fan Chung, is a Taiwanese-born mathematician who works mainly in the areas of spectral graph theory[?] and extremal graph theory[?].
		(See graph theory.) She is currently the Akamai Professor in Internet Mathematics at the University of California, San Diego (UCSD) in the United States.
		Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, No. 92), American Mathematical Society, 1997, ISBN 0-8218-0315-8
	www.termsdefined.net /fa/fan-chung.html (300 words)

	The Graph Theorists' Home Page Guide
		First of all, if you're a graph theorist or some person with strong interest in graph theory (you need not to be a mathematician!), and if you have a homepage but don't find a link to it on this page, please contact me as described above.
		PIGALE is a graph editor with an interface to the LEDA library and with many algorithms implemented essentially concerning planar graphs.
		"Graph Theory and Its Applications" (together with Jay Yellen), "a comprehensive applications-driven textbook that provides material for several different courses in graph theory." This site also provides links to other graph theoretical and mathematical resources.
	www.joergzuther.de /math/graph/homes.html (8696 words)

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