Signatures of small-world and scale-free properties in large computer programs

A large computer program is typically divided into many hundreds or even thousands of smaller units, whose logical connections define a network in a natural way. This network reflects the internal structure of the program, and defines the "information flow" within the program. We show that (1) due to its growth in time this network displays a scale-free feature in that the probability of the number of links at a node obeys a power-law distribution, and (2) as a result of performance optimization of the program the network has a small-world structure. We believe that these features are generic for large computer programs. Our work extends the previous studies on growing networks, which have mostly been for physical networks, to the domain of computer software.

[1]  B Skyrms,et al.  A dynamic model of social network formation. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

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

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

[4]  S N Dorogovtsev,et al.  Effect of the accelerating growth of communications networks on their structure. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[6]  D. Fell,et al.  The small world of metabolism , 2000, Nature Biotechnology.

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

[8]  M. Newman,et al.  Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[10]  K. Tamura,et al.  Metabolic engineering of plant alkaloid biosynthesis. Proc Natl Acad Sci U S A , 2001 .

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

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

[13]  Nature Genetics , 1991, Nature.

[14]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

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

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

[17]  M E Newman,et al.  Scientific collaboration networks. I. Network construction and fundamental results. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  U. Blum,et al.  Religion and economic growth: was Weber right? , 2001 .

[19]  S. N. Dorogovtsev,et al.  Scaling properties of scale-free evolving networks: continuous approach. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[21]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[22]  Partha Dasgupta,et al.  Topology of the conceptual network of language. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  B. Kogut.  The network as knowledge : Generative rules and the emergence of structure , 2000 .

[24]  R. May,et al.  How Viruses Spread Among Computers and People , 2001, Science.

[25]  B. Kogut,et al.  The Small World of Germany and the Durability of National Networks , 2001, American Sociological Review.

[26]  P. Bourgine,et al.  Topological and causal structure of the yeast transcriptional regulatory network , 2002, Nature Genetics.

[27]  Moshe Gitterman,et al.  Small-world phenomena in physics: the Ising model , 2000 .

[28]  B. Tadić.  Dynamics of directed graphs: the world-wide Web , 2000, cond-mat/0011442.

[29]  Gesine Reinert,et al.  Small worlds , 2001, Random Struct. Algorithms.

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

[31]  M. Keeling,et al.  The effects of local spatial structure on epidemiological invasions , 1999, Proceedings of the Royal Society of London. Series B: Biological Sciences.

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

[33]  M. Gell-Mann,et al.  Physics Today. , 1966, Applied optics.

[34]  M. Young,et al.  Computational analysis of functional connectivity between areas of primate cerebral cortex. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[35]  A. Barabasi,et al.  Scale-free characteristics of random networks: the topology of the world-wide web , 2000 .

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

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

[38]  A. Blumen,et al.  Relaxation of disordered polymer networks: Regular lattice made up of small-world Rouse networks , 2001 .

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

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