Revisiting "scale-free" networks.

Recent observations of power-law distributions in the connectivity of complex networks came as a big surprise to researchers steeped in the tradition of random networks. Even more surprising was the discovery that power-law distributions also characterize many biological and social networks. Many attributed a deep significance to this fact, inferring a "universal architecture" of complex systems. Closer examination, however, challenges the assumptions that (1) such distributions are special and (2) they signify a common architecture, independent of the system's specifics. The real surprise, if any, is that power-law distributions are easy to generate, and by a variety of mechanisms. The architecture that results is not universal, but particular; it is determined by the actual constraints on the system in question.

[1]  Charles Gide,et al.  Cours d'économie politique , 1911 .

[2]  G. Yule,et al.  A Mathematical Theory of Evolution, Based on the Conclusions of Dr. J. C. Willis, F.R.S. , 1925 .

[3]  G. Yule,et al.  A Mathematical Theory of Evolution Based on the Conclusions of Dr. J. C. Willis, F.R.S. , 1925 .

[4]  Alfred J. Lotka,et al.  The frequency distribution of scientific productivity , 1926 .

[5]  George Kingsley Zipf,et al.  Human behavior and the principle of least effort , 1949 .

[6]  J. Marchal Cours d'economie politique , 1950 .

[7]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[8]  H. Simon,et al.  ON A CLASS OF SKEW DISTRIBUTION FUNCTIONS , 1955 .

[9]  D J PRICE,et al.  NETWORKS OF SCIENTIFIC PAPERS. , 1965, Science.

[10]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[11]  R. Merton The Matthew Effect in Science , 1968, Science.

[12]  Derek de Solla Price,et al.  A general theory of bibliometric and other cumulative advantage processes , 1976, J. Am. Soc. Inf. Sci..

[13]  L. Engwall Skew distributions and the sizes of business firms , 1976 .

[14]  H. A. Simon,et al.  Skew Distributions and the Size of Business Firms , 1977 .

[15]  G. Wolters,et al.  Concepts, Theories, and Rationality in the Biological Sciences , 1995 .

[16]  Benoit B. Mandelbrot,et al.  Fractals and Scaling in Finance , 1997 .

[17]  R. Brandon Does Biology Have Laws? The Experimental Evidence , 1997, Philosophy of Science.

[18]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[19]  Ravi Kumar,et al.  Extracting Large-Scale Knowledge Bases from the Web , 1999, VLDB.

[20]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[21]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[22]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[23]  A. Levine,et al.  Surfing the p53 network , 2000, Nature.

[24]  J. Levine,et al.  Surfing the p53 network , 2000, Nature.

[25]  R. Albert,et al.  The large-scale organization of metabolic networks , 2000, Nature.

[26]  Eli Upfal,et al.  Stochastic models for the Web graph , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[27]  S. Wuchty Scale-free behavior in protein domain networks. , 2001, Molecular biology and evolution.

[28]  E. Koonin,et al.  Scale-free networks in biology: new insights into the fundamentals of evolution? , 2002, BioEssays : news and reviews in molecular, cellular and developmental biology.

[29]  Albert-László Barabási,et al.  Linked: The New Science of Networks , 2002 .

[30]  Walter Willinger,et al.  Scaling phenomena in the Internet: Critically examining criticality , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[31]  A. Barabasi,et al.  Hierarchical Organization of Modularity in Metabolic Networks , 2002, Science.

[32]  Maximino Aldana-Gonzalez,et al.  Linked: The New Science of Networks , 2003 .

[33]  Duncan J. Watts,et al.  Six Degrees: The Science of a Connected Age , 2003 .

[34]  James R. Knight,et al.  A Protein Interaction Map of Drosophila melanogaster , 2003, Science.

[35]  Michael Mitzenmacher,et al.  A Brief History of Generative Models for Power Law and Lognormal Distributions , 2004, Internet Math..

[36]  Fan Chung Graham,et al.  The Average Distance in a Random Graph with Given Expected Degrees , 2004, Internet Math..

[37]  J. Doyle,et al.  Bow Ties, Metabolism and Disease , 2022 .

[38]  Walter Willinger,et al.  A first-principles approach to understanding the internet's router-level topology , 2004, SIGCOMM '04.

[39]  Justin A. Ionita,et al.  Metabolic networks: enzyme function and metabolite structure. , 2004, Current opinion in structural biology.

[40]  S. L. Wong,et al.  A Map of the Interactome Network of the Metazoan C. elegans , 2004, Science.

[41]  A. Barabasi,et al.  Network biology: understanding the cell's functional organization , 2004, Nature Reviews Genetics.

[42]  Walter Willinger,et al.  More "normal" than normal: scaling distributions and complex systems , 2004, Proceedings of the 2004 Winter Simulation Conference, 2004..

[43]  Arun K. Ramani,et al.  Protein interaction networks from yeast to human. , 2004, Current opinion in structural biology.

[44]  M. Cobb Making sense of life: explaining biological development with models, metaphors and machines , 2004, Heredity.

[45]  Massimo Marchiori,et al.  Error and attacktolerance of complex network s , 2004 .

[46]  M. Gerstein,et al.  Genomic analysis of regulatory network dynamics reveals large topological changes , 2004, Nature.

[47]  Walter Willinger,et al.  Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications , 2005, Internet Math..