Generalized preferential attachment considering aging

Preferential Attachment (PA) models the scientific citation process. In the PA model, a new paper attaches itself to the citation network based only on the popularity of the currently existing papers. This invariably leads to a network whose degree distribution satisfies the Power Law. Yet, empirical results show that paper age should also play a role in the citation process. In other words, when references are chosen for a new paper, the age of an existing paper may also affect the choice for citing. In this paper, we derive a generalized PA model that includes the effect of aging, with analytical solution. Such a model can be used to analyze the competing influence of preferential attachment and aging effect quantitatively in citation process and explain differences in various research domains by the extent of aging. It may also serve as a general model of network formation.

[1]  Ying Wang,et al.  The citation networks model with random aging , 2012, Complex..

[2]  K. Hajra,et al.  Modelling aging characteristics in citation networks , 2005, physics/0508035.

[3]  J. D. Tardós,et al.  Publish or Perish , 1987 .

[4]  M. Newman,et al.  Coauthorship and citation patterns in the Physical Review. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[6]  Hamid Bouabid,et al.  Revisiting citation aging: a model for citation distribution and life-cycle prediction , 2011, Scientometrics.

[7]  Kamalika Basu Hajra,et al.  Aging in citation networks , 2004, cond-mat/0409017.

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

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

[10]  L. Egghe.  Power Laws in the Information Production Process: Lotkaian Informetrics , 2005 .

[11]  Eli Upfal,et al.  Stochastic models for the Web graph , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

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

[13]  Thijs Pollman,et al.  Forgetting and the Ageing of Scientific Publications , 2004, Scientometrics.

[14]  Steve Pressé,et al.  Nonuniversal power law scaling in the probability distribution of scientific citations , 2010, Proceedings of the National Academy of Sciences.

[15]  Eli Upfal,et al.  Using PageRank to Characterize Web Structure , 2002, COCOON.

[16]  S. Redner.  Citation statistics from 110 years of physical review , 2005, physics/0506056.

[17]  Jon Kleinberg,et al.  Authoritative sources in a hyperlinked environment , 1999, SODA '98.

[18]  Christos Faloutsos,et al.  Graph mining: Laws, generators, and algorithms , 2006, CSUR.

[19]  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.

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

[21]  Christos Faloutsos,et al.  Graphs over time: densification laws, shrinking diameters and possible explanations , 2005, KDD '05.

[22]  Leo Egghe,et al.  General evolutionary theory of information production processes and applications to the evolution of networks , 2007, J. Informetrics.

[23]  John D. Lafferty,et al.  Dynamic topic models , 2006, ICML.

[24]  Ying Ding,et al.  The distribution of references across texts: Some implications for citation analysis , 2013, J. Informetrics.

[25]  Santo Fortunato,et al.  Characterizing and Modeling Citation Dynamics , 2011, PloS one.

[26]  Philip M. Morse,et al.  Methods of Mathematical Physics , 1947, The Mathematical Gazette.

[27]  Lutz Bornmann,et al.  What do citation counts measure? A review of studies on citing behavior , 2008, J. Documentation.

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

[29]  G. Bianconi.  Emergence of weight-topology correlations in complex scale-free networks , 2004, cond-mat/0412399.

[30]  Daren Yu,et al.  Effect of the age of papers on the preferential attachment in citation networks , 2009 .

[31]  F. J. Pierce,et al.  Contemporary Statistical Models for the Plant and Soil Sciences , 2001 .

[32]  David M. Blei,et al.  Probabilistic topic models , 2012, Commun. ACM.

[33]  Daren Yu,et al.  Measuring the preferential attachment mechanism in citation networks , 2008 .

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

[35]  Ravi Kumar,et al.  Extracting Large-Scale Knowledge Bases from the Web , 1999, VLDB.

[36]  M. White,et al.  A Qualitative Study of Citing Behavior: Contributions, Criteria, and Metalevel Documentation Concerns , 1997, The Library Quarterly.

[37]  S. N. Dorogovtsev,et al.  Minimal models of weighted scale-free networks , 2004 .

[38]  Han Zhu,et al.  Effect of aging on network structure. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Daniel Jurafsky,et al.  Who should I cite: learning literature search models from citation behavior , 2010, CIKM.

[40]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[41]  Dah-Ming Chiu,et al.  "Publish or Perish" in the Internet Age: a study of publication statistics in computer networking research , 2010, CCRV.

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