Com_Overview - arXiv:cond-mat/0303516v1...

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Unformatted text preview: arXiv:cond-mat/0303516v1 [cond-mat.stat-mech] 25 Mar 2003 The structure and function of complex networks M. E. J. Newman Department of Physics, University of Michigan, Ann Arbor, MI 48109, U.S.A. and Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, U.S.A. Inspired by empirical studies of networked systems such as the Internet, social networks, and bio- logical networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks. Contents Acknowledgments 1 I. Introduction 2 A. Types of networks 3 B. Other resources 4 C. Outline of the review 4 II. Networks in the real world 4 A. Social networks 5 B. Information networks 6 C. Technological networks 8 D. Biological networks 8 III. Properties of networks 9 A. The small-world effect 9 B. Transitivity or clustering 11 C. Degree distributions 12 1. Scale-free networks 13 2. Maximum degree 14 D. Network resilience 15 E. Mixing patterns 16 F. Degree correlations 17 G. Community structure 17 H. Network navigation 19 I. Other network properties 19 IV. Random graphs 20 A. Poisson random graphs 20 B. Generalized random graphs 22 1. The configuration model 22 2. Example: power-law degree distribution 23 3. Directed graphs 24 4. Bipartite graphs 24 5. Degree correlations 25 V. Exponential random graphs and Markov graphs 26 VI. The small-world model 27 A. Clustering coefficient 28 B. Degree distribution 28 C. Average path length 29 VII. Models of network growth 30 A. Prices model 30 B. The model of Barab asi and Albert 31 C. Generalizations of the Barab asiAlbert model 34 D. Other growth models 35 E. Vertex copying models 37 VIII. Processes taking place on networks 37 A. Percolation theory and network resilience 38 B. Epidemiological processes 40 1. The SIR model 40 2. The SIS model 42 C. Search on networks 43 1. Exhaustive network search 43 2. Guided network search 44 3. Network navigation 45 D. Phase transitions on networks 46 E. Other processes on networks 47 IX. Summary and directions for future research 47 References 48 Acknowledgments For useful feedback on early versions of this article, the author would particularly like to thank Lada Adamic, Michelle Girvan, Petter Holme, Randy LeVeque, Sidney Redner, Ricard Sol e, Steve Strogatz, Alexei V azquez, and an anonymous referee. For other helpful conversations and comments about networks thanks go to Lada Adamic, L aszl o Barab asi, Stefan Bornholdt, Duncan Callaway, Peter Dodds, Jennifer Dunne, Rick Durrett, Stephanie Forrest, Michelle Girvan, Jon Kleinberg, James Moody, Cris Moore, Martina Morris, Juyong Park, Richard Rothenberg, Larry Ruzzo, Matthew Salganik, Len Sander, Steve...
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Com_Overview - arXiv:cond-mat/0303516v1...

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