Generating scale-free networks with adjustable clustering coefficient via random walks

This paper presents an algorithm for generating scale-free networks with adjustable clustering coefficient. The algorithm is based on a random walk procedure combined with a triangle generation scheme which takes into account genetic factors; this way, preferential attachment and clustering control are implemented using only local information. Simulations are presented which support the validity of the scheme, characterizing its tuning capabilities.

[1]  A. Barabasi,et al.  Evolution of the social network of scientific collaborations , 2001, cond-mat/0104162.

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

[3]  M. Weigt,et al.  On the properties of small-world network models , 1999, cond-mat/9903411.

[4]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[5]  Albert-László Barabási,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW , 2004 .

[6]  N. Johnson,et al.  Realistic network growth using only local information: From random to scale-free and beyond , 2006, cond-mat/0608733.

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

[8]  S. Brenner,et al.  The structure of the nervous system of the nematode Caenorhabditis elegans. , 1986, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[9]  Z. Di,et al.  Emergence of global preferential attachment from local interaction , 2009, 0910.0103.

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

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

[12]  A. Vázquez.  Knowing a network by walking on it: emergence of scaling , 2000, cond-mat/0006132.

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

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

[15]  Eli Upfal,et al.  The Web as a graph , 2000, PODS.

[16]  A-L Barabási,et al.  Structure and tie strengths in mobile communication networks , 2006, Proceedings of the National Academy of Sciences.

[17]  T. Evans,et al.  Scale-free networks from self-organization. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[19]  A. Vázquez,et al.  Network clustering coefficient without degree-correlation biases. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  J. Jost,et al.  Evolving networks with distance preferences. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  K. Kaski,et al.  Scale-free networks generated by random walkers , 2004, cond-mat/0404088.

[22]  B. Bollobás.  The evolution of random graphs , 1984 .

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

[24]  Marián Boguñá,et al.  Tuning clustering in random networks with arbitrary degree distributions. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  K. Kaski,et al.  A Model For Social Networks , 2006, physics/0601114.

[26]  Krishna P. Gummadi,et al.  Measurement and analysis of online social networks , 2007, IMC '07.

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

[28]  Walter Willinger,et al.  The origin of power laws in Internet topologies revisited , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[29]  Sergey N. Dorogovtsev,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW (Physics) , 2003 .

[30]  Beom Jun Kim,et al.  Growing scale-free networks with tunable clustering. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[32]  N. Christakis,et al.  A Model of Genetic Variation in Human Social Networks , 2010 .

[33]  Stefan Bornholdt,et al.  Emergence of a small world from local interactions: modeling acquaintance networks. , 2002, Physical review letters.

[34]  Mark E. J. Newman,et al.  Random graphs containing arbitrary distributions of subgraphs , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Ian T. Foster,et al.  Mapping the Gnutella Network: Properties of Large-Scale Peer-to-Peer Systems and Implications for System Design , 2002, ArXiv.

[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]  A. Vázquez.  Growing network with local rules: preferential attachment, clustering hierarchy, and degree correlations. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.