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Comparison to Existing Models

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Citation Analysis and Dynamics of Citation Networks

Part of the book series: SpringerBriefs in Complexity ((BRIEFSCOMPLEXITY))

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Abstract

We make a survey of models of citation dynamics and focus on the preferential attachment and fitness models. We show that under certain realistic conditions these models are equivalent. In order to find the microscopic foundations of the preferential attachment mechanism, we analyze theoretically and experimentally several citation networks and demonstrate that, for a broad fitness distribution, this mechanism reduces to the fitness model. The fitness model yields the long-sought explanation for the initial attractivity K 0, an elusive parameter which was left unexplained within the framework of the empirical preferential attachment model. We show that the initial attractivity is determined by the width of the fitness distribution. We compare the preferential attachment and fitness models to our microscopic model of citation dynamics based on recursive search and show that our model contains both these phenomenological models.

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References

  1. Albert, R., & Barabasi, A. L. (2002). Statistical mechanics of complex networks. Reviews of Modern Physics, 74, 47–97.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Bagrow, J. P., & Brockmann, D. (2013). Natural emergence of clusters and bursts in network evolution. Physical Review X, 3, 021016.

    Article  ADS  Google Scholar 

  3. Barabasi, A. L. (2015). Network science. Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  4. Barabasi, A. L., Song, C., & Wang D. (2012). Publishing: Handful of papers dominates citation. Nature, 491(7422), 40.

    Article  ADS  Google Scholar 

  5. Bedogne, C., & Rodgers, G. J. (2006). Complex growing networks with intrinsic vertex fitness. Physical Review E, 74(4), 046115.

    Article  ADS  Google Scholar 

  6. Bell, M., Perera, S., Piraveenan, M., Bliemer, M., Latty, T., & Reid, C. (2017). Network growth models: A behavioural basis for attachment proportional to fitness. Scientific Reports, 7, 42431.

    Article  ADS  Google Scholar 

  7. Bianconi, G., & Barabasi, A.-L. (2001). Bose-Einstein condensation in complex networks. Physical Review Letters, 86, 5632–5635.

    Article  ADS  Google Scholar 

  8. Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., & Hwang, D.-U. (2006). Complex networks: Structure and dynamics. Physics Reports, 424(4–5), 175–308.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Bramoullé, Y., Currarini, S., Jackson, M. O., Pin, P., & Rogers, B. W. (2012). Homophily and long-run integration in social networks. Journal of Economic Theory, 147(5), 1754–1786.

    Article  MathSciNet  MATH  Google Scholar 

  10. Burrell, Q. L. (2003). Predicting future citation behavior. Journal of the American Society for Information Science and Technology, 54(5), 372–378.

    Article  Google Scholar 

  11. Caldarelli, G. (2007). Scale-free networks: Complex webs in nature and technology. Oxford: Oxford University Press.

    Book  MATH  Google Scholar 

  12. Caldarelli, G., Capocci, A., De Los Rios, P., & Muñoz, M. A. (2002). Scale-free networks from varying vertex intrinsic fitness. Physical Review Letters, 89(25), 258702.

    Article  ADS  Google Scholar 

  13. Capocci, A., Servedio, V. D., Colaiori, F., Buriol, L. S., Donato, D., Leonardi, S., et al. (2006). Preferential attachment in the growth of social networks: The internet encyclopedia Wikipedia. Physical Review E, 74(3), 036116.

    Article  ADS  Google Scholar 

  14. Carletti, T., Gargiulo, F., & Lambiotte, R. (2015). Preferential attachment with partial information. The European Physical Journal B, 88(1), 18.

    Article  ADS  Google Scholar 

  15. Centola, D. (2010). The spread of behavior in an online social network experiment. Science, 329(5996), 1194–1197.

    Article  ADS  Google Scholar 

  16. Centola, D., Eguíluz, V. M., & Macy, M. W. (2007). Cascade dynamics of complex propagation. Physica A: Statistical Mechanics and Its Applications, 374(1), 449–456.

    Article  ADS  Google Scholar 

  17. Ciotti, V., Bonaventura, M., Nicosia, V., Panzarasa, P., & Latora, V. (2016). Homophily and missing links in citation networks. EPJ Data Science, 5(1), 7.

    Article  Google Scholar 

  18. Csárdi, G., Strandburg, K. J., Zalányi, L., Tobochnik, J., & Érdi, P. (2007). Modeling innovation by a kinetic description of the patent citation system. Physica A: Statistical Mechanics and Its Applications, 374(2), 783–793.

    Article  ADS  Google Scholar 

  19. Dorogovtsev, S. N., & Mendes, J. F. F. (2000). Evolution of networks with aging of sites. Physical Review E, 62(2), 1842–1845.

    Article  ADS  Google Scholar 

  20. Eom, Y.-H., & Fortunato, S. (2011). Characterizing and modeling citation dynamics. PLoS One, 6(9), e24926.

    Article  ADS  Google Scholar 

  21. Ergün, G., & Rodgers, G. J. (2002). Growing random networks with fitness. Physica A: Statistical Mechanics and Its Applications, 303(1), 261–272.

    Article  ADS  MATH  Google Scholar 

  22. Fortunato, S., Flammini, A., & Menczer, F. (2006). Scale-free network growth by ranking. Physical Review Letters, 96(21), 218701.

    Article  ADS  Google Scholar 

  23. Geng, X., & Wang, Y. (2009). Degree correlations in citation networks model with aging. Europhysics Letters, 88(3), 38002.

    Article  ADS  MathSciNet  Google Scholar 

  24. Ghadge, S., Killingback, T., Sundaram, B., & Tran, D. A. (2010). A statistical construction of power-law networks. International Journal of Parallel, Emergent and Distributed Systems, 25(3), 223–235.

    Article  MathSciNet  MATH  Google Scholar 

  25. Gleeson, J. P., Cellai, D., Onnela, J.-P., Porter, M. A., & Reed-Tsochas, F. (2014). A simple generative model of collective online behavior. Proceedings of the National Academy of Sciences, 111(29), 10411–10415.

    Article  ADS  Google Scholar 

  26. Goldberg, S. R., Anthony, H., & Evans, T. S. (2015). Modelling citation networks. Scientometrics, 105(3), 1577–1604.

    Article  Google Scholar 

  27. Golosovsky, M. (2017). Power-law citation distributions are not scale-free. Physical Review E, 96(3), 032306.

    Article  ADS  Google Scholar 

  28. Golosovsky, M. (2018). Mechanisms of complex network growth: Synthesis of the preferential attachment and fitness models. Physical Review E, 97(6), 062310.

    Article  ADS  Google Scholar 

  29. Golosovsky, M., & Solomon, S. (2012). Stochastic dynamical model of a growing citation network based on a self-exciting point process. Physical Review Letters, 109(9), 098701.

    Article  ADS  Google Scholar 

  30. Golosovsky, M., & Solomon, S. (2013). The transition towards immortality: Non-linear autocatalytic growth of citations to scientific papers. Journal of Statistical Physics, 151(1–2), 340–354.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. Golosovsky, M., & Solomon, S. (2017). Growing complex network of citations of scientific papers: Modeling and measurements. Physical Review E, 95(1), 012324.

    Article  ADS  Google Scholar 

  32. Hajra, K. B., & Sen, P. (2006). Modelling aging characteristics in citation networks. Physica A: Statistical Mechanics and Its Applications, 368(2), 575–582.

    Article  ADS  Google Scholar 

  33. Higham, K. W., Governale, M., Jaffe, A. B., & Zülicke, U. (2017). Fame and obsolescence: Disentangling growth and aging dynamics of patent citations. Physical Review E, 95(4), 042309.

    Article  ADS  Google Scholar 

  34. Higham, K. W., Governale, M., Jaffe, A. B., & Zülicke, U. (2017). Unraveling the dynamics of growth, aging and inflation for citations to scientific articles from specific research fields. Journal of Informetrics, 11(4), 1190–1200.

    Article  Google Scholar 

  35. Jackson, M. O., & Rogers, B. W. (2007). Meeting strangers and friends of friends: How random are social networks? American Economic Review, 97(3), 890–915.

    Article  Google Scholar 

  36. Jeong, H., Néda, Z., & Barabási, A.-L. (2003). Measuring preferential attachment in evolving networks. Europhysics Letters, 61(4), 567–572.

    Article  ADS  Google Scholar 

  37. Ke, Q., Ferrara, E., Radicchi, F., & Flammini, A. (2015). Defining and identifying sleeping beauties in science. Proceedings of the National Academy of Sciences, 112(24), 7426–7431.

    Article  ADS  Google Scholar 

  38. Kong, J. S., Sarshar, N., & Roychowdhury, V. P. (2008). Experience versus talent shapes the structure of the Web. Proceedings of the National Academy of Sciences, 105(37), 13724–13729.

    Article  ADS  Google Scholar 

  39. Krapivsky, P. L., & Redner, S. (2001). Organization of growing random networks. Physical Review E, 63(6), 066123.

    Article  ADS  Google Scholar 

  40. Krapivsky, P. L., & Redner, S. (2005). Network growth by copying. Physical Review E, 71, 036118.

    Article  ADS  Google Scholar 

  41. Kunegis, J., Blattner, M., & Moser, C. (2013). Preferential attachment in online networks. In Proceedings of the 5th Annual ACM Web Science Conference. New York, NY: Association for Computing Machinery.

    Google Scholar 

  42. Lambiotte, R., & Ausloos, M. (2007). Growing network with j-redirection. Europhysics Letters, 77(5), 58002.

    Article  ADS  MathSciNet  Google Scholar 

  43. Lambiotte, R., Krapivsky, P. L., Bhat, U., & Redner, S. (2016). Structural transitions in densifying networks. Physical Review Letters, 117(21), 218301.

    Article  ADS  Google Scholar 

  44. Leskovec, J., Backstrom, L., Kumar, R., & Tomkins, A. (2008). Microscopic evolution of social networks. In Proceeding of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD 08. New York, NY: Association for Computing Machinery.

    Google Scholar 

  45. Leskovec, J., Kleinberg, J., & Faloutsos, C. (2005). Graphs over time. In Proceeding of the Eleventh ACM SIGKDD International Conference on Knowledge Discovery in Data Mining - KDD 05. New York, NY: Association for Computing Machinery.

    Google Scholar 

  46. Liben-Nowell, D., & Kleinberg, J. (2003). The link prediction problem for social networks. In Proceedings of the Twelfth International Conference on Information and Knowledge Management - CIKM. New York, NY: Association for Computing Machinery.

    Google Scholar 

  47. Luck, J. M., & Mehta, A. (2017). How the fittest compete for leadership: A tale of tails. Physical Review E, 95(6), 062306.

    Article  ADS  Google Scholar 

  48. Martin, T., Ball, B., Karrer, B., & Newman, M. E. J. (2013). Coauthorship and citation patterns in the physical review. Physical Review E, 88(1), 012814.

    Article  ADS  Google Scholar 

  49. Medo, M., Cimini, G., & Gualdi, S. (2011). Temporal effects in the growth of networks. Physical Review Letters, 107, 238701.

    Article  ADS  Google Scholar 

  50. Menczer, F. (2004). Evolution of document networks. Proceedings of the National Academy of Sciences, 101(Supplement 1), 5261–5265.

    Article  ADS  Google Scholar 

  51. Miller, B. A., & Bliss, N. T. (2012). A stochastic system for large network growth. IEEE Signal Processing Letters, 19(6), 356–359.

    Article  ADS  Google Scholar 

  52. Mislove A., Koppula H. S., Gummadi K. P., Druschel P., & Bhattacharjee B. (2013). An empirical validation of growth models for complex networks. In A. Mukherjee, M. Choudhury, F. Peruani, N. Ganguly, & B. Mitra (Eds.), Dynamics on and of complex networks. Modeling and simulation in science, engineering and technology (Vol. 2). New York, NY: Birkhäuser.

    Google Scholar 

  53. Mokryn, O., Wagner, A., Blattner, M., Ruppin, E., & Shavitt, Y. (2016). The role of temporal trends in growing networks. PLoS One, 11(8), e0156505.

    Article  Google Scholar 

  54. Newman, M. (2010). Networks. Oxford: Oxford University Press.

    Book  MATH  Google Scholar 

  55. Newman, M. E. (2001). Clustering and preferential attachment in growing networks. Physical Review E, 64(2), 025102.

    Article  ADS  Google Scholar 

  56. Newman, M. E. J. (2009). The first-mover advantage in scientific publication. Europhysics Letters, 86(6), 68001.

    Article  ADS  Google Scholar 

  57. Newman, M. E. J. (2014). Prediction of highly cited papers. Europhysics Letters, 105(2), 28002.

    Article  ADS  Google Scholar 

  58. Nguyen, K., & Tran, D. A. (2012). Fitness-based generative models for power-law networks. In Handbook of optimization in complex networks (pp. 39–53). Berlin: Springer.

    Chapter  Google Scholar 

  59. Ostroumova-Prokhorenkova, L., & Samosvat, E. (2016). Recency-based preferential attachment models. Journal of Complex Networks, 4(4), 475–499.

    MathSciNet  Google Scholar 

  60. Papadopoulos, F., Kitsak, M., Serrano, M. Á., Boguñá, M., & Krioukov, D. (2012). Popularity versus similarity in growing networks. Nature, 489(7417), 537–540.

    Article  ADS  Google Scholar 

  61. Perc, M. (2014).The Matthew effect in empirical data. Journal of the Royal Society Interface, 11, 20140378.

    Article  Google Scholar 

  62. Pham, T., Sheridan, P., & Shimodaira, H. (2015). PAFit: A statistical method for measuring preferential attachment in temporal complex networks. PLoS One, 10(9), e0137796.

    Article  Google Scholar 

  63. Pham, T., Sheridan, P., & Shimodaira, H. (2016). Joint estimation of preferential attachment and node fitness in growing complex networks. Scientific Reports, 6, 32558.

    Article  ADS  Google Scholar 

  64. Price, D. D. S. (1976). A general theory of bibliometric and other cumulative advantage processes. Journal of the American Society for Information Science, 27(5), 292–306.

    Article  Google Scholar 

  65. Redner, S. (2005). Citation statistics from 110 years of Physical Review. Physics Today, 58(6), 49–54.

    Article  Google Scholar 

  66. Rosvall, M., Esquivel, A. V., Lancichinetti, A., West, J. D., & Lambiotte, R. (2014). Memory in network flows and its effects on spreading dynamics and community detection. Nature Communications, 5, 4630.

    Article  ADS  Google Scholar 

  67. Sendiña-Nadal, I., Danziger, M. M., Wang, Z., Havlin, S., & Boccaletti, S. (2016). Assortativity and leadership emerge from anti-preferential attachment in heterogeneous networks. Scientific Reports, 6(1), 21297.

    Article  ADS  Google Scholar 

  68. Servedio, V. D. P., Caldarelli, G., & Buttà, P. (2004). Vertex intrinsic fitness: How to produce arbitrary scale-free networks. Physical Review E, 70(5), 056126.

    Article  ADS  Google Scholar 

  69. Simkin, M. V., & Roychowdhury, V. P. (2007). A mathematical theory of citing. Journal of the American Society for Information Science and Technology, 58(11), 1661–1673.

    Article  Google Scholar 

  70. Šubelj, L., & Bajec, M. (2013). Model of complex networks based on citation dynamics. In Proceedings of the WWW Workshop on Large Scale Network Analysis, 2013:(LSNA’13) (pp.527–530).

    Google Scholar 

  71. Vazquez, A. (2001). Disordered networks generated by recursive searches. Europhysics Letters, 54(4), 430–435.

    Article  ADS  Google Scholar 

  72. Wang, D., Song, C., & Barabsi, A. L. (2013). Quantifying long-term scientific impact. Science, 342(6154), 127–132.

    Article  ADS  Google Scholar 

  73. Wang, M., Yu, G., & Yu, D. (2008). Measuring the preferential attachment mechanism in citation networks. Physica A: Statistical Mechanics and Its Applications, 387(18), 4692–4698.

    Article  ADS  Google Scholar 

  74. Wu, Y., Fu, T. Z. J., & Chiu, D. M. (2014). Generalized preferential attachment considering aging. Journal of Informetrics, 8(3), 650–658.

    Article  Google Scholar 

  75. Wu, Z.-X., & Holme, P. (2009). Modeling scientific-citation patterns and other triangle-rich acyclic networks. Physical Review E, 80, 037101.

    Article  ADS  Google Scholar 

  76. Xie, Z., Ouyang, Z., Liu, Q., & Li, J. (2016). A geometric graph model for citation networks of exponentially growing scientific papers. Physica A: Statistical Mechanics and Its Applications, 456, 167–175.

    Article  ADS  Google Scholar 

  77. Zhou, J., Zeng, A., Fan, Y., & Di, Z. (2016) Ranking scientific publications with similarity-preferential mechanism. Scientometrics, 106(2), 805–816.

    Article  Google Scholar 

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  1. Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem, Israel

    Michael Golosovsky

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Golosovsky, M. (2019). Comparison to Existing Models. In: Citation Analysis and Dynamics of Citation Networks. SpringerBriefs in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-28169-4_9

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