A statistical physics perspective on Web growth

Abstract Approaches from statistical physics are applied to investigate the structure of network models whose growth rules mimic aspects of the evolution of the World Wide Web. We first determine the degree distribution of a growing network in which nodes are introduced one at a time and attach to an earlier node of degree k with rate Ak∼kγ. Very different behaviors arise for γ 1. We also analyze the degree distribution of a heterogeneous network, the joint age-degree distribution, the correlation between degrees of neighboring nodes, as well as global network properties. An extension to directed networks is then presented. By tuning model parameters to reasonable values, we obtain distinct power-law forms for the in-degree and out-degree distributions with exponents that are in good agreement with current data for the web. Finally, a general growth process with independent introduction of nodes and links is investigated. This leads to independently growing sub-networks that may coalesce with other sub-networks. General results for both the size distribution of sub-networks and the degree distribution are obtained.

[1]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[2]  D. Sornette,et al.  Stretched exponential distributions in nature and economy: “fat tails” with characteristic scales , 1998, cond-mat/9801293.

[3]  Huberman,et al.  Strong regularities in world wide web surfing , 1998, Science.

[4]  G. Caldarelli,et al.  The fractal properties of Internet , 2000, cond-mat/0009178.

[5]  S. Redner,et al.  Organization of growing random networks. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  William Shockley,et al.  On the Statistics of Individual Variations of Productivity in Research Laboratories , 1957, Proceedings of the IRE.

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

[8]  Andrei Z. Broder,et al.  Graph structure in the Web , 2000, Comput. Networks.

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

[10]  Bruce A. Reed,et al.  A Critical Point for Random Graphs with a Given Degree Sequence , 1995, Random Struct. Algorithms.

[11]  Svante Janson,et al.  Random graphs , 2000, ZOR Methods Model. Oper. Res..

[12]  H. Simon,et al.  Models of Man. , 1957 .

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

[14]  Béla Bollobás,et al.  Random Graphs , 1985 .

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

[16]  M. Basta,et al.  An introduction to percolation , 1994 .

[17]  Cohen,et al.  Resilience of the internet to random breakdowns , 2000, Physical review letters.

[18]  Albert,et al.  Topology of evolving networks: local events and universality , 2000, Physical review letters.

[19]  S. Redner.  How popular is your paper? An empirical study of the citation distribution , 1998, cond-mat/9804163.

[20]  S. N. Dorogovtsev,et al.  Scaling Behaviour of Developing and Decaying Networks , 2000, cond-mat/0005050.

[21]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[22]  J. Hopcroft,et al.  Are randomly grown graphs really random? , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  J. Villain,et al.  Physics of crystal growth , 1998 .

[24]  Ronald L. Graham,et al.  Concrete mathematics - a foundation for computer science , 1991 .

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

[26]  Bruce A. Reed,et al.  The Size of the Giant Component of a Random Graph with a Given Degree Sequence , 1998, Combinatorics, Probability and Computing.

[27]  S Redner,et al.  Degree distributions of growing networks. , 2001, Physical review letters.

[28]  Ibrahim Matta,et al.  On the origin of power laws in Internet topologies , 2000, CCRV.

[29]  E. Garfield.  Citation analysis as a tool in journal evaluation. , 1972, Science.

[30]  J. Kertész,et al.  Preferential growth: exact solution of the time-dependent distributions. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Luciano Pietronero,et al.  FRACTALS IN PHYSICS , 1990 .

[32]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[33]  A. Bray.  Theory of phase-ordering kinetics , 1994, cond-mat/9501089.

[34]  Lada A. Adamic,et al.  Internet: Growth dynamics of the World-Wide Web , 1999, Nature.

[35]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[36]  M. Newman,et al.  Random graphs with arbitrary degree distributions and their applications. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Walter Willinger,et al.  Does AS size determine degree in as topology? , 2001, CCRV.

[38]  Ginestra Bianconi,et al.  Competition and multiscaling in evolving networks , 2001 .

[39]  S. N. Dorogovtsev,et al.  Anomalous percolation properties of growing networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.