Emergence of tempered preferential attachment from optimization

We show how preferential attachment can emerge in an optimization framework, resolving a long-standing theoretical controversy. We also show that the preferential attachment model so obtained has two novel features, saturation and viability, which have natural interpretations in the underlying network and lead to a power-law degree distribution with exponential cutoff. Moreover, we consider a generalized version of this preferential attachment model with independent saturation and viability, leading to a broader class of power laws again with exponential cutoff. We present a collection of empirical observations from social, biological, physical, and technological networks, for which such degree distributions give excellent fits. We suggest that, in general, optimization models that give rise to preferential attachment with saturation and viability effects form a good starting point for the analysis of many networks.

[1]  Deryk Osthus,et al.  Popularity based random graph models leading to a scale-free degree sequence , 2004, Discret. Math..

[2]  J M Carlson,et al.  Highly optimized tolerance: a mechanism for power laws in designed systems. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  M. Newman,et al.  The structure of scientific collaboration networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

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

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

[6]  G. Pólya,et al.  Über die Statistik verketteter Vorgänge , 1923 .

[7]  Christian Borgs,et al.  Competition-Induced Preferential Attachment , 2004, ICALP.

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

[9]  Christos H. Papadimitriou,et al.  Heuristically Optimized Trade-Offs: A New Paradigm for Power Laws in the Internet , 2002, ICALP.

[10]  S. N. Dorogovtsev,et al.  Structure of growing networks with preferential linking. , 2000, Physical review letters.

[11]  公庄 庸三.  Discrete math = 離散数学 , 2004 .

[12]  Alessandro Vespignani,et al.  Exploring networks with traceroute-like probes: theory and simulations , 2004, Theor. Comput. Sci..

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

[14]  Chadi Barakat,et al.  Controlled use of excess backbone bandwidth for providing new services in IP-over-WDM networks , 2004, IEEE Journal on Selected Areas in Communications.

[15]  S. Low,et al.  The "robust yet fragile" nature of the Internet. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[17]  Yan Y. Kagan,et al.  Observational evidence for earthquakes as a nonlinear dynamic process , 1994 .

[18]  Fan Chung Graham,et al.  Duplication Models for Biological Networks , 2002, J. Comput. Biol..

[19]  Jeremy Sweet,et al.  Hybridization Between Brassica napus and B. rapa on a National Scale in the United Kingdom , 2003, Science.

[20]  김삼묘,et al.  “Bioinformatics” 특집을 내면서 , 2000 .

[21]  Y. Kagan,et al.  Earthquakes Cannot Be Predicted , 1997, Science.

[22]  K. Pearson.  Biometrika , 1902, The American Naturalist.

[23]  David J. Galas,et al.  A duplication growth model of gene expression networks , 2002, Bioinform..

[24]  Robert L. Goldstone,et al.  The simultaneous evolution of author and paper networks , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[25]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[26]  Alan M. Frieze,et al.  A general model of web graphs , 2003, Random Struct. Algorithms.

[27]  Christian Borgs,et al.  Degree Distribution of Competition-Induced Preferential Attachment Graphs , 2005, Combinatorics, Probability and Computing.

[28]  Béla Bollobás,et al.  The degree sequence of a scale‐free random graph process , 2001, Random Struct. Algorithms.

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

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

[31]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[32]  S. Redner,et al.  Connectivity of growing random networks. , 2000, Physical review letters.