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Author : Zbigniew Palka
Publisher :
ISBN 13 :
Total Pages : 120 pages
Book Rating : 4.3/5 (121 download)
Download or read book Asymptotic Properties of Random Graphs written by Zbigniew Palka and published by . This book was released on 1988 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alan Frieze
Publisher : Cambridge University Press
ISBN 13 : 1107118506
Total Pages : 483 pages
Book Rating : 4.1/5 (71 download)
Download or read book Introduction to Random Graphs written by Alan Frieze and published by Cambridge University Press. This book was released on 2016 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.
Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 1139460889
Total Pages : 203 pages
Book Rating : 4.1/5 (394 download)
Download or read book Random Graph Dynamics written by Rick Durrett and published by Cambridge University Press. This book was released on 2010-05-31 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.
Author : Remco van der Hofstad
Publisher : Cambridge University Press
ISBN 13 : 110717287X
Total Pages : 341 pages
Book Rating : 4.1/5 (71 download)
Download or read book Random Graphs and Complex Networks written by Remco van der Hofstad and published by Cambridge University Press. This book was released on 2017 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.
Author : Manfred Schwaiger
Publisher : Springer Science & Business Media
ISBN 13 : 364255721X
Total Pages : 547 pages
Book Rating : 4.6/5 (425 download)
Download or read book Exploratory Data Analysis in Empirical Research written by Manfred Schwaiger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a selection of new methods and approaches in the field of Exploratory Data Analysis. The reader will find numerous ideas and examples for cross disciplinary applications of classification and data analysis methods in fields such as data and web mining, medicine and biological sciences as well as marketing, finance and management sciences.
Author : Svante Janson
Publisher : John Wiley & Sons
ISBN 13 : 1118030966
Total Pages : 350 pages
Book Rating : 4.1/5 (18 download)
Download or read book Random Graphs written by Svante Janson and published by John Wiley & Sons. This book was released on 2011-09-30 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified, modern treatment of the theory of random graphs-including recent results and techniques Since its inception in the 1960s, the theory of random graphs has evolved into a dynamic branch of discrete mathematics. Yet despite the lively activity and important applications, the last comprehensive volume on the subject is Bollobas's well-known 1985 book. Poised to stimulate research for years to come, this new work covers developments of the last decade, providing a much-needed, modern overview of this fast-growing area of combinatorics. Written by three highly respected members of the discrete mathematics community, the book incorporates many disparate results from across the literature, including results obtained by the authors and some completely new results. Current tools and techniques are also thoroughly emphasized. Clear, easily accessible presentations make Random Graphs an ideal introduction for newcomers to the field and an excellent reference for scientists interested in discrete mathematics and theoretical computer science. Special features include: * A focus on the fundamental theory as well as basic models of random graphs * A detailed description of the phase transition phenomenon * Easy-to-apply exponential inequalities for large deviation bounds * An extensive study of the problem of containing small subgraphs * Results by Bollobas and others on the chromatic number of random graphs * The result by Robinson and Wormald on the existence of Hamilton cycles in random regular graphs * A gentle introduction to the zero-one laws * Ample exercises, figures, and bibliographic references
Author : Béla Bollobás
Publisher : Cambridge University Press
ISBN 13 : 9780521797221
Total Pages : 520 pages
Book Rating : 4.7/5 (972 download)
Download or read book Random Graphs written by Béla Bollobás and published by Cambridge University Press. This book was released on 2001-08-30 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a revised and updated version of the classic first edition.
Author : Michael Krivelevich
Publisher : Cambridge University Press
ISBN 13 : 1107136571
Total Pages : 129 pages
Book Rating : 4.1/5 (71 download)
Download or read book Random Graphs, Geometry and Asymptotic Structure written by Michael Krivelevich and published by Cambridge University Press. This book was released on 2016-04-25 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise introduction, aimed at young researchers, to recent developments of a geometric and topological nature in random graphs.
Author : Alan Frieze
Publisher : Cambridge University Press
ISBN 13 : 1009260316
Total Pages : 234 pages
Book Rating : 4.0/5 (92 download)
Download or read book Random Graphs and Networks: A First Course written by Alan Frieze and published by Cambridge University Press. This book was released on 2023-03-09 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Networks surround us, from social networks to protein–protein interaction networks within the cells of our bodies. The theory of random graphs provides a necessary framework for understanding their structure and development. This text provides an accessible introduction to this rapidly expanding subject. It covers all the basic features of random graphs – component structure, matchings and Hamilton cycles, connectivity and chromatic number – before discussing models of real-world networks, including intersection graphs, preferential attachment graphs and small-world models. Based on the authors' own teaching experience, it can be used as a textbook for a one-semester course on random graphs and networks at advanced undergraduate or graduate level. The text includes numerous exercises, with a particular focus on developing students' skills in asymptotic analysis. More challenging problems are accompanied by hints or suggestions for further reading.
Author : James Vincent Schultz
Publisher :
ISBN 13 :
Total Pages : 224 pages
Book Rating : 4.:/5 (89 download)
Download or read book The Approximate Sampling Distributions for Certain Asymptotic Properties of Random Graphs written by James Vincent Schultz and published by . This book was released on 1974 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Percy Deift
Publisher : American Mathematical Soc.
ISBN 13 : 0821826956
Total Pages : 273 pages
Book Rating : 4.8/5 (218 download)
Download or read book Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach written by Percy Deift and published by American Mathematical Soc.. This book was released on 2000 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random n times n matrices exhibit universal behavior as n > infinity? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems. Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.
Author : Geoffrey Grimmett
Publisher : Cambridge University Press
ISBN 13 : 1108542999
Total Pages : 279 pages
Book Rating : 4.1/5 (85 download)
Download or read book Probability on Graphs written by Geoffrey Grimmett and published by Cambridge University Press. This book was released on 2018-01-25 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Author : V. F. Kolchin
Publisher : Cambridge University Press
ISBN 13 : 0521440815
Total Pages : 266 pages
Book Rating : 4.5/5 (214 download)
Download or read book Random Graphs written by V. F. Kolchin and published by Cambridge University Press. This book was released on 1999 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results of research on classical combinatorial structures such as random graphs, permutations, and systems of random linear equations in finite fields.
Author : Xueliang Li
Publisher : Springer Science & Business Media
ISBN 13 : 1461442206
Total Pages : 270 pages
Book Rating : 4.4/5 (614 download)
Download or read book Graph Energy written by Xueliang Li and published by Springer Science & Business Media. This book was released on 2012-08-10 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about graph energy. The authors have included many of the important results on graph energy, such as the complete solution to the conjecture on maximal energy of unicyclic graphs, the Wagner-Heuberger’s result on the energy of trees, the energy of random graphs or the approach to energy using singular values. It contains an extensive coverage of recent results and a gradual development of topics and the inclusion of complete proofs from most of the important recent results in the area. The latter fact makes it a valuable reference for researchers looking to get into the field of graph energy, further stimulating it with occasional inclusion of open problems. The book provides a comprehensive survey of all results and common proof methods obtained in this field with an extensive reference section. The book is aimed mainly towards mathematicians, both researchers and doctoral students, with interest in the field of mathematical chemistry.
Author : Brigitte Chauvin
Publisher : Birkhäuser
ISBN 13 : 3034882114
Total Pages : 526 pages
Book Rating : 4.0/5 (348 download)
Download or read book Mathematics and Computer Science II written by Brigitte Chauvin and published by Birkhäuser. This book was released on 2012-12-06 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume in a series of innovative proceedings entirely devoted to the connections between mathematics and computer science. Here mathematics and computer science are directly confronted and joined to tackle intricate problems in computer science with deep and innovative mathematical approaches. The book serves as an outstanding tool and a main information source for a large public in applied mathematics, discrete mathematics and computer science, including researchers, teachers, graduate students and engineers. It provides an overview of the current questions in computer science and the related modern and powerful mathematical methods. The range of applications is very wide and reaches beyond computer science.
Author : Mark Newman
Publisher : Princeton University Press
ISBN 13 : 0691113572
Total Pages : 593 pages
Book Rating : 4.6/5 (911 download)
Download or read book The Structure and Dynamics of Networks: written by Mark Newman and published by Princeton University Press. This book was released on 2006-05-07 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Internet to networks of friendship, disease transmission, and even terrorism, the concept--and the reality--of networks has come to pervade modern society. But what exactly is a network? What different types of networks are there? Why are they interesting, and what can they tell us? In recent years, scientists from a range of fields--including mathematics, physics, computer science, sociology, and biology--have been pursuing these questions and building a new "science of networks." This book brings together for the first time a set of seminal articles representing research from across these disciplines. It is an ideal sourcebook for the key research in this fast-growing field. The book is organized into four sections, each preceded by an editors' introduction summarizing its contents and general theme. The first section sets the stage by discussing some of the historical antecedents of contemporary research in the area. From there the book moves to the empirical side of the science of networks before turning to the foundational modeling ideas that have been the focus of much subsequent activity. The book closes by taking the reader to the cutting edge of network science--the relationship between network structure and system dynamics. From network robustness to the spread of disease, this section offers a potpourri of topics on this rapidly expanding frontier of the new science.
Author : Jaroslav Nešetřil
Publisher : American Mathematical Soc.
ISBN 13 : 1470440652
Total Pages : 120 pages
Book Rating : 4.4/5 (74 download)
Download or read book A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth written by Jaroslav Nešetřil and published by American Mathematical Soc.. This book was released on 2020-04-03 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors introduce a general framework for the study of limits of relational structures and graphs in particular, which is based on a combination of model theory and (functional) analysis. The authors show how the various approaches to graph limits fit to this framework and that the authors naturally appear as “tractable cases” of a general theory. As an outcome of this, the authors provide extensions of known results. The authors believe that this puts these into a broader context. The second part of the paper is devoted to the study of sparse structures. First, the authors consider limits of structures with bounded diameter connected components and prove that in this case the convergence can be “almost” studied component-wise. They also propose the structure of limit objects for convergent sequences of sparse structures. Eventually, they consider the specific case of limits of colored rooted trees with bounded height and of graphs with bounded tree-depth, motivated by their role as “elementary bricks” these graphs play in decompositions of sparse graphs, and give an explicit construction of a limit object in this case. This limit object is a graph built on a standard probability space with the property that every first-order definable set of tuples is measurable. This is an example of the general concept of modeling the authors introduce here. Their example is also the first “intermediate class” with explicitly defined limit structures where the inverse problem has been solved.
