Deterministic scale-free networks

Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are stochastic, that is they create networks in which the nodes appear to be randomly connected to each other. Here we propose a simple model that generates scale-free networks in a deterministic fashion. We solve exactly the model, showing that the tail of the degree distribution follows a power law.

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

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

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

[4]  A.Bianconi,et al.  Limits on the low-energy antinucleon-nucleus annihilations from the Heisenberg principle , 2001 .

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

[6]  Albert-László Barabási,et al.  The physics of the Web , 2001 .

[7]  S. N. Dorogovtsev,et al.  Exactly solvable small-world network , 1999, cond-mat/9907445.

[8]  A. Barabasi,et al.  Bose-Einstein condensation in complex networks. , 2000, Physical review letters.

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

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

[11]  B. Mandelbrot.  Fractal Geometry of Nature , 1984 .

[12]  S. N. Dorogovtsev,et al.  Evolution of networks with aging of sites , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[14]  L. Amaral,et al.  The web of human sexual contacts , 2001, Nature.

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

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

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

[18]  Mark Newman,et al.  Models of the Small World , 2000 .

[19]  Reka Albert,et al.  Mean-field theory for scale-free random networks , 1999 .

[20]  J. M. Oshorn.  Proc. Nat. Acad. Sei , 1978 .

[21]  A. Barabasi,et al.  Lethality and centrality in protein networks , 2001, Nature.

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

[23]  T. Vicsek.  Fractal Growth Phenomena , 1989 .