From the architecture of the Internet to the spreading of an epidemic

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In recent years, statistical physicists have begun to apply their methods to problems stemming from disciplines which are not theirs, such as the dynamic laws governing the growth of the Internet. This monograph is a contribution to the emerging field of complex networks, i.e. the study of the dynamic and statistical properties of systems composed of many nodes connected by links. After reviewing the topological properties shared by many real large networks along with the most popular models, a number of questions are discussed from a statistical physics perspective: Why does the map of the Internet have to be interpreted carefully? How does its local topology influence the spread of computer viruses? Under what circumstances is it possible to build a network that is both efficient and inexpensive, when a cost has to be borne for establishing physical links between the nodes? This book will prove useful to all scientists interested in seeing an example of how traditional approaches can successfully be applied to present-day challenges.

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