Time-invariant degree growth in preferential attachment network models

Preferential attachment drives the evolution of many complex networks. Its analytical studies mostly consider the simplest case of a network that grows uniformly in time despite the accelerating growth of many real networks. Motivated by the observation that the average degree growth of nodes is time invariant in empirical network data, we study the degree dynamics in the relevant class of network models where preferential attachment is combined with heterogeneous node fitness and aging. We propose an analytical framework based on the time invariance of the studied systems and show that it is self-consistent only for two special network growth forms: the uniform and the exponential network growth. Conversely, the breaking of such time invariance explains the winner-takes-all effect in some model settings, revealing the connection between the Bose-Einstein condensation in the Bianconi-Barabási model and similar gelation in superlinear preferential attachment. Aging is necessary to reproduce realistic node degree growth curves and can prevent the winner-takes-all effect under weak conditions. Our results are verified by extensive numerical simulations.

[1]  M. Newman.  Clustering and preferential attachment in growing networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Béla Bollobás,et al.  The degree sequence of a scale‐free random graph process , 2001, Random Struct. Algorithms.

[3]  Steffen Staab,et al.  Decay of Relevance in Exponentially Growing Networks , 2018, WebSci.

[4]  Albert-László Barabási,et al.  Quantifying Long-Term Scientific Impact , 2013, Science.

[5]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[6]  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.

[7]  Jie Tang,et al.  ArnetMiner: extraction and mining of academic social networks , 2008, KDD.

[8]  Jon M. Kleinberg,et al.  The Web as a Graph: Measurements, Models, and Methods , 1999, COCOON.

[9]  Lada A. Adamic,et al.  Power-Law Distribution of the World Wide Web , 2000, Science.

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

[11]  Giulio Cimini,et al.  Temporal effects in the growth of networks , 2011, Physical review letters.

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

[13]  M. A. Muñoz,et al.  Scale-free networks from varying vertex intrinsic fitness. , 2002, Physical review letters.

[14]  SpencerJoel,et al.  The degree sequence of a scale-free random graph process , 2001 .

[15]  G. B. A. Barab'asi.  Competition and multiscaling in evolving networks , 2000, cond-mat/0011029.

[16]  Matús Medo,et al.  Statistical validation of high-dimensional models of growing networks , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  J. Mattick,et al.  Accelerating, hyperaccelerating, and decelerating networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Z. Neda,et al.  Measuring preferential attachment in evolving networks , 2001, cond-mat/0104131.

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

[20]  Michael Ley,et al.  The DBLP Computer Science Bibliography: Evolution, Research Issues, Perspectives , 2002, SPIRE.

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

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

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

[24]  M. E. J. Newman,et al.  The first-mover advantage in scientific publication , 2008, 0809.0522.

[25]  Ed H. Chi,et al.  The singularity is not near: slowing growth of Wikipedia , 2009, Int. Sym. Wikis.

[26]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[27]  G. Caldarelli,et al.  Preferential attachment in the growth of social networks, the Internet encyclopedia wikipedia , 2007 .

[28]  Santo Fortunato,et al.  Attention Decay in Science , 2015, J. Informetrics.