Finite-Time Fluctuations in the Degree Statistics of Growing Networks

This paper presents a comprehensive analysis of the degree statistics in models for growing networks where new nodes enter one at a time and attach to one earlier node according to a stochastic rule. The models with uniform attachment, linear attachment (the Barabási-Albert model), and generalized preferential attachment with initial attractiveness are successively considered. The main emphasis is on finite-size (i.e., finite-time) effects, which are shown to exhibit different behaviors in three regimes of the size-degree plane: stationary, finite-size scaling, large deviations.

[1]  Alessandro Vespignani,et al.  Dynamical Processes on Complex Networks , 2008 .

[2]  Alessandro Vespignani,et al.  Cut-offs and finite size effects in scale-free networks , 2003, cond-mat/0311650.

[3]  S. Redner,et al.  Finiteness and fluctuations in growing networks , 2002, cond-mat/0207107.

[4]  K. Pearson,et al.  Biometrika , 1902, The American Naturalist.

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

[6]  J. M. Luck,et al.  Nonequilibrium dynamics of urn models , 2002 .

[7]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

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

[9]  Nonequilibrium dynamics of the zeta urn model , 2001 .

[10]  J. Luck,et al.  A record-driven growth process , 2008, 0809.3377.

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

[12]  S Redner,et al.  Statistics of changes in lead node in connectivity-driven networks. , 2002, Physical review letters.

[13]  D J PRICE,et al.  NETWORKS OF SCIENTIFIC PAPERS. , 1965, Science.

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

[15]  Z. Burda,et al.  Statistical ensemble of scale-free random graphs. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  I M Sokolov,et al.  Finite-size effects in Barabási-Albert growing networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  S. N. Dorogovtsev,et al.  Size-dependent degree distribution of a scale-free growing network. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[20]  Dynamics of condensation in zero-range processes , 2003, cond-mat/0301156.

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

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

[23]  Sarika Jalan,et al.  Analytical results for stochastically growing networks: connection to the zero-range process. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[25]  S. Coulomb,et al.  Asymmetric evolving random networks , 2002, cond-mat/0212371.

[26]  G. Bianconi,et al.  Dynamics of condensation in growing complex networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

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