Princeton University Press
The Structure and Dynamics of Networks
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About this book
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.
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Frontmatter
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Contents
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Preface
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Chapter One. Introduction
1 - Chapter Two. Historical developments
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Chain-links
21 -
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Connectivity of random nets
27 -
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On the evolution of random graphs
38 -
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Contacts and influence
83 -
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An experimental study of the small world problem
130 -
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Networks of scientific papers
149 -
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Famous trails to Paul Erdös
155 - Chapter 3. Empirical Studies
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Diameter of the world-wide web
182 -
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Graph structure in the web
183 -
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On power-law relationships of the internet topology
195 -
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Classes of small-world networks
207 -
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The large-scale organization of metabolic networks
211 -
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The small world of metabolism
215 -
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Network Motifs: Simple Building Blocks of Complex Networks
217 -
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The structure of scientific collaboration networks
221 -
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The web of human sexual contacts
227 - Chapter 4. Models of networks
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4.1 RANDOM GRAPH MODELS
229 -
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A Critical Point for Random Graphs with a Given Degree Sequence
240 -
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A Random Graph Model for Massive Graphs
259 -
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Random graphs with arbitrary degree distributions and their applications
269 -
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4.2 THE SMALL-WORLD MODEL
286 -
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Collective dynamics of 'small-world' networks
301 -
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Small-World Networks: Evidence for a Crossover Picture
304 -
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Comment on "Small-world networks: Evidence for crossover picture"
308 -
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Scaling and percolation in the small-world network model
310 -
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On the properties of small-world network models
321 -
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4.3 MODELS OF SCALE-FREE NETWORKS
335 -
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Emergence of Scaling in Random Networks
349 -
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Structure of Growing Networks with Preferential Linking
353 -
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Connectivity of Growing Ra ndom Networks
357 -
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Competition and multiscaling m evolving networks
361 -
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Universal Behavior of Load Distribution in Scale-Free Networks
368 -
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Spectra of "real-world" graphs: Beyond the semicircle law
372 -
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The Degree Sequence of a Scale-Free Random Graph Process
384 -
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A MODEL OF LARGE-SCALE PROTEOME EVOLUTION
396 -
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Modeling of Protein Interaction Networks
408 - Chapter Five. Applications
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5.1 EPIDEMICS AND RUMORS
415 -
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5.2 ROBUSTNESS OF NETWORKS
424 -
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5.3 SEARCHING NETWORKS
428 -
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EPIDEMICS WITH TWO LEVELS OF MIXING
436 -
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The effects of local spatial structure on epidemiological invasions
480 -
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Small World Effect in an Epidemiological Model
489 -
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Epidemic Spreading in Scale-Free Networks
493 -
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A simple model of global cascades on random networks
497 -
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Error and attack tolerance of complex networks
503 -
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Resilience of the Internet to Random Breakdowns
507 -
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Network Robustness and Fragility: Percolation on Random Graphs
510 -
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Authoritative Sources in a Hyperlinked Environment
514 -
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Search in power-law networks
543 -
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Navigation in a small world
551 -
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Chapter Six. Outlook
553 -
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References
559 -
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Index
575