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Books on the topic 'Graph theory techniques'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Diagram techniques in group theory. Cambridge [England]: Cambridge University Press, 1990.

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2

Irniger, Christophe-André Mario. Graph matching: Filtering databases of graphs using machine learning techniques. Berlin: AKA, 2005.

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3

1949-, Kanō Mikio, ed. Factors and factorizations of graphs: Proof techniques in factor theory. Heidelberg: Springer Verlag, 2011.

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4

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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5

Image processing and analysis with graphs: Theory and practice. Boca Raton, FL: Taylor & Francis, 2012.

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6

Symposium on Graph Drawing (11th 2003 Perugia, Italy). Graph drawing: 11th international symposium, GD 2003, Perugia, Italy, September 21-24, 2003 : revised papers. Berlin: Springer, 2004.

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7

D, Liotta Giuseppe Ph, ed. Graph drawing: 11th international symposium, GD 2003, Perugia, Italy, September 21-24, 2003 : revised papers. Berlin: Springer, 2004.

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8

Sebastian, Rudolph, Wilson Nic, Howse John, Corby Olivier, and SpringerLink (Online service), eds. Graph Structures for Knowledge Representation and Reasoning: Second International Workshop, GKR 2011, Barcelona, Spain, July 16, 2011. Revised Selected Papers. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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9

Lin, I.-Jong. Video object extraction and representation: Theory and applications. Boston, Mass: Kluwer Academic Publisher, 2000.

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10

Aigner, Martin. Combinatorial search. Stuttgart: B.G. Teubner, 1988.

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11

Alberto, Corso, and Polini Claudia 1966-, eds. Commutative algebra and its connections to geometry: Pan-American Advanced Studies Institute, August 3--14, 2009, Universidade Federal de Pernambuco, Olinda, Brazil. Providence, R.I: American Mathematical Society, 2011.

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12

Adam, Schenker, ed. Graph-theoretic techniques for web content mining. Hackensack, N.J: World Scientific, 2005.

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13

Weighted graph based ordering techniques for preconditioned conjugate gradient methods. [Moffett Field, Calif.]: Research Institute for Advanced Computer Science, NASA Ames Research Center, 1994.

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14

Smith, David K. Networks and Graphs: Techniques and Computational Methods. Horwood Publishing Limited, 2003.

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15

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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16

Grady, Leo, and Olivier Lezoray. Image Processing and Analysis with Graphs: Theory and Practice. Taylor & Francis Group, 2017.

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17

Grady, Leo, and Olivier Lezoray. Image Processing and Analysis with Graphs: Theory and Practice. Taylor & Francis Group, 2017.

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18

Coolen, A. C. C., A. Annibale, and E. S. Roberts. Soft constraints: exponential random graph models. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0004.

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Exponential random graph models (ERGMs) provide conceptually elegant recipes for generating soft-constrained random graphs. This chapter begins by explaining the theory and describing how to properly specify an ERGM, including demonstrating Lagrange’s method to derive the values of the model parameters that correspond to the desired constraints. Three ERGMs, all with constraints depending linearly on the adjacency matrix, are solved exactly: the targeted total number of links, targeted individual node degrees and targeted number of two-way links in a directed graph. However, when the controlled features become more complicated, ERGMs have a tendency to produce graphs in extreme phases (very dense or very sparse). The two-star model and the Strauss model are worked through in detail using advanced techniques from statistical mechanics in order to analyze the phase transitions. The chapter closes with a discussion of the strengths and weaknesses of ERGMs as null models.

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19

Graph-Theoretic Techniques for Web Content Mining (Machine Perception and Artificial Intelligence) (Series in Machine Perception and Artificial Intelligence). World Scientific Publishing Company, 2005.

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20

Lyman, R. Lee. Graphing Culture Change in North American Archaeology. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198871156.001.0001.

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Documentation, analysis, and explanation of culture change have long been goals of archaeology. The earliest archaeological spindle graphs appeared in the 1880s and 1890s, but had no influence on subsequent archaeologists. Line graphs showing change in frequencies of specimens in each of several artifact types were used in the 1910s and 1920s. Seriograms or straight-sided spindles diagraming interpretations of culture change were published in the 1930s, but were seldom subsequently mimicked. Spindle graphs of centered and stacked columns of bars, each column representing a distinct artifact type, each bar the empirically documented relative frequency of specimens in an assemblage, were developed in the 1940s, became popular in the 1950s and 1960s, and are often used to illustrate culture change in textbooks published during the twentieth century. Graphs facilitate visual thinking, different graph types suggest different ontologies and theories of change, and particular techniques of parsing temporally continuous morphological variation of artifacts into types influence graph form. Line graphs, bar graphs, spindle diagrams, and phylogenetic trees of artifacts and cultures indicate archaeologists often mixed elements of Darwinian variational evolutionary change with elements of Midas-touch-like transformational change. Today there is minimal discussion of graph theory or graph grammar in both introductory archaeology textbooks and advanced texts, and elements of the two theories of evolution are often mixed. Culture has changed, and despite archaeology’s unique access to the totality of humankind’s cultural past, there is minimal discussion on graph theory, construction, and decipherment in the archaeological literature.

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21

P, Chen E., Luk V. K, American Society of Mechanical Engineers. Applied Mechanics Division., and American Society of Mechanical Engineers. Winter Meeting, eds. Advances in numerical simulation techniques for penetration and perforation of solids: Presented at the 1993 ASME Winter Annual Meeting New Orleans, Louisiana November 28-December 3, 1993. New York, N.Y: American Society of Mechanical Engineers, 1993.

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22

Qamber, Isa S. H. Markov modelling of equipment behaviour: General behaviour of plant and equipment described by Markov processes arestudied using graph theory, Kronecker matrices, transforms and numerical techniques. Bradford, 1987.

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23

Coolen, Ton, Alessia Annibale, and Ekaterina Roberts. Generating Random Networks and Graphs. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.001.0001.

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This book supports researchers who need to generate random networks, or who are interested in the theoretical study of random graphs. The coverage includes exponential random graphs (where the targeted probability of each network appearing in the ensemble is specified), growth algorithms (i.e. preferential attachment and the stub-joining configuration model), special constructions (e.g. geometric graphs and Watts Strogatz models) and graphs on structured spaces (e.g. multiplex networks). The presentation aims to be a complete starting point, including details of both theory and implementation, as well as discussions of the main strengths and weaknesses of each approach. It includes extensive references for readers wishing to go further. The material is carefully structured to be accessible to researchers from all disciplines while also containing rigorous mathematical analysis (largely based on the techniques of statistical mechanics) to support those wishing to further develop or implement the theory of random graph generation. This book is aimed at the graduate student or advanced undergraduate. It includes many worked examples, numerical simulations and exercises making it suitable for use in teaching. Explicit pseudocode algorithms are included to make the ideas easy to apply. Datasets are becoming increasingly large and network applications wider and more sophisticated. Testing hypotheses against properly specified control cases (null models) is at the heart of the ‘scientific method’. Knowledge on how to generate controlled and unbiased random graph ensembles is vital for anybody wishing to apply network science in their research.

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24

Sorrentino, Alfonso. From KAM Theory to Aubry-Mather Theory. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691164502.003.0002.

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This chapter discusses an illustrative example, namely the properties of invariant probability measures and orbits on KAM tori (or more generally, on invariant Lagrangian graphs). This will prepare the ground for understanding the main ideas and techniques that will be developed in the following chapters, without several technicalities that might be confusing to a neophyte.

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25

Rudolph, Sebastian, Pierre Marquis, Madalina Croitoru, and Gem Stapleton. Graph Structures for Knowledge Representation and Reasoning: 5th International Workshop, GKR 2017, Melbourne, VIC, Australia, August 21, 2017, Revised ... Springer, 2018.

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26

Rudolph, Sebastian, Pierre Marquis, Madalina Croitoru, and Gem Stapleton. Graph Structures for Knowledge Representation and Reasoning: 4th International Workshop, GKR 2015, Buenos Aires, Argentina, July 25, 2015, Revised ... Springer, 2016.

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27

Wang, Jason T. L., Bruce A. Shapiro, and Dennis Shasha, eds. Pattern Discovery in Biomolecular Data. Oxford University Press, 1999. http://dx.doi.org/10.1093/oso/9780195119404.001.0001.

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Finding patterns in biomolecular data, particularly in DNA and RNA, is at the center of modern biological research. These data are complex and growing rapidly, so the search for patterns requires increasingly sophisticated computer methods. Pattern Discovery in Biomolecular Data provides a clear, up-to-date summary of the principal techniques. Each chapter is self-contained, and the techniques are drawn from many fields, including graph theory, information theory, statistics, genetic algorithms, computer visualization, and vision. Since pattern searches often benefit from multiple approaches, the book presents methods in their purest form so that readers can best choose the method or combination that fits their needs. The chapters focus on finding patterns in DNA, RNA, and protein sequences, finding patterns in 2D and 3D structures, and choosing system components. This volume will be invaluable for all workers in genomics and genetic analysis, and others whose research requires biocomputing.

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28

Verbaarschot, Jac. Quantum chaos and quantum graphs. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.33.

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This article examines the origins of the universality of the spectral statistics of quantum chaotic systems in the context of periodic orbit theory. It also considers interesting analogies between periodic orbit theory and the sigma model, along with related work on quantum graphs. The article first reviews some facts and definitions for classically chaotic systems in order to elucidate their quantum behaviour, focusing on systems with two degrees of freedom: one characterized by ergodicity and another by hyperbolicity. It then describes two semiclassical approximation techniques — Gutzwiller’s periodic orbit theory and a refined approach incorporating the unitarity of the quantum evolution — and highlights their importance in understanding universal spectral statistics, and how they are related to the sigma model. This is followed by an analysis of parallel developments for quantum graphs, which are relevant to quantum chaos.

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29

Kung, S. Y., and I.-Jong Lin. Video Object Extraction and Representation: Theory and Applications (The Springer International Series in Engineering and Computer Science). Springer, 2000.

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30

Tanasa, Adrian. Combinatorial Physics. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895493.001.0001.

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After briefly presenting (for the physicist) some notions frequently used in combinatorics (such as graphs or combinatorial maps) and after briefly presenting (for the combinatorialist) the main concepts of quantum field theory (QFT), the book shows how algebraic combinatorics can be used to deal with perturbative renormalisation (both in commutative and non-commutative quantum field theory), how analytic combinatorics can be used for QFT issues (again, for both commutative and non-commutative QFT), how Grassmann integrals (frequently used in QFT) can be used to proCve new combinatorial identities (generalizing the Lindström–Gessel–Viennot formula), how combinatorial QFT can bring a new insight on the celebrated Jacobian conjecture (which concerns global invertibility of polynomial systems) and so on. In the second part of the book, matrix models, and tensor models are presented to the reader as QFT models. Several tensor model results (such as the implementation of the large N limit and of the double-scaling limit for various such tensor models, N being here the size of the tensor) are then exposed. These results are natural generalizations of results extensively used by theoretical physicists in the study of matrix models and they are obtained through intensive use of combinatorial techniques (this time mainly enumerative techniques). The last part of the book is dedicated to the recently discovered relation between tensor models and the holographic Sachdev–Ye–Kitaev model, model which has been extensively studied in the last years by condensed matter and by high-energy physicists.

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