Evolution of Networks: From Biological Nets to the Internet and WWW

OUP Oxford
3
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We live in a world of networks, where everything is amazingly close to everything else. The notion of 'network' turns out to be central to our times: the Internet and WWW are changing our lives; our physical existence is based on various biological networks; we are involved in all-enveloping networks of economic and social relations. Only in the 1990s did physicists begin to explore real networks, both natural and artificial, as evolving systems with intriguingly complex and effective architectures. Progress has been so immediate and astounding that we actually face a new science based on a new set of concepts, and, one may even say, on a new philosophy: the natural philosophy of a small world. Old ideas from mathematics, statistical physics, biology, computer science, and so on take on quite new forms in applications to real evolving networks. - What is common to all networks? - What are the general principles of the organization and evolution of networks? - How do the laws of nature work in communication, biological, and social networks? - What are networks? This book, written by physicists, answers these questions and presents a general insight into the world of networks.
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Additional Information

Publisher
OUP Oxford
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Published on
Nov 14, 2013
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Pages
280
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ISBN
9780191004407
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Best For
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Language
English
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Genres
Business & Economics / Economics / General
Computers / Hardware / General
Computers / Networking / General
Computers / Neural Networks
Computers / Software Development & Engineering / Systems Analysis & Design
Language Arts & Disciplines / Library & Information Science / General
Language Arts & Disciplines / Linguistics / General
Mathematics / Applied
Mathematics / Combinatorics
Science / Life Sciences / Biology
Science / Physics / Condensed Matter
Science / Physics / General
Science / Physics / Mathematical & Computational
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Content Protection
This content is DRM protected.
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Eligible for Family Library

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In the context of network theory, Complex networks can be de?ned as a collection of nodes connected by edges representing various complex int- actions among the nodes. Almost any large-scale system, be it natural or man-made, can be viewed as a complex network of interacting entities, which is dynamically evolving over time. Naturally occurring networks include - ological, ecological and social networks (e. g. , metabolic networks, gene r- ulatory networks, protein interaction networks, signaling networks, epidemic networks, food webs, scienti?c collaboration networks and acquaintance n- works), whereas man-made networks include communication networks and transportation infrastructures (e. g. , the Internet, the World Wide Web, pe- to-peer networks, power grids and airline networks). This edited volume is a sequel to the workshop Dynamics on and of C- plex Networks (http://www. cel. iitkgp. ernet. in/?eccs07/) held as a satellite event of the fourth European Conference on Complex Systems in Dresden, Germany from October 1–5, 2007. The primary aim of this workshop was to systematically explore the statistical dynamics “on” and “of” complex n- works that prevail across a large number of scienti?c disciplines. Dynamics on networks refers to the di?erent types of processes, for instance, prolife- tion and di?usion, that take place on networks. The functionality/e?ciency of these processes is strongly tied to the underlying topology as well as the dynamic behavior of the network.
The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed account of newer topics, including Szemer\'edi's Regularity Lemma and its use, Shelah's extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. In no other branch of mathematics is it as vital to tackle and solve challenging exercises in order to master the subject. To this end, the book contains an unusually large number of well thought-out exercises: over 600 in total. Although some are straightforward, most of them are substantial, and others will stretch even the most able reader.
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