-
维弗雷多·帕累托(Vilfredo Pareto, 1848−1923),福利经济学先驱;乔治·金斯利·齐普夫(George Kingsley Zipf, 1902−1950),计量语言学先驱;德里克·普莱斯(Derek John de Solla Price, 1922−1983),科学计量学之父;赫伯特·亚历山大·西蒙(Herbert Alexander Simon, 1916−2001),人工智能先驱;波努瓦·曼德布罗特(Benoit B. Mandelbrot, 1924−2010),分形之父;艾伯特-拉斯洛·巴拉巴西(Albert-László Barabási, 1967−),当今网络科学研究代表人物、无标度网络概念提出者。如果能够把这些横跨3个世纪、来自不同领域的科学先驱组织在一起召开主题论坛的话,他们讨论甚至争论的主题也许只有一个:幂律分布。本文通过围绕网络科学中的核心概念——无标度网络、幂律分布以及偏好链接机制的“多次重复发现”和“多轮争议”的故事,与读者分享网络科学研究的曲折而又动人的历程。
在科学发展史上,同一个科学发现,以不同的形式、在不同的时间和不同的地点、被不同的科学家重新发现并引起争议的例子屡见不鲜,其中的原因包括:一是由于交流不够广泛,使得不少学术成果难以为更多的研究人员所了解;二是由于认识不够深入,开始以为是不同的东西,逐渐才能揭示出共同的本质。无标度网络无疑属于网络科学过去20年发展中最重要的概念之一,甚至不少人觉得可以把“之一”两字去掉。而无标度网络及其对应的幂律分布和偏好链接的“多次重复发明”和“多轮争议”作为体现科学发展历程的生动例子确实值得一说。
从网络科学的眼光看,这些研究和争议本身就串成了一个网络,本文希望能够让更多的读者体验到这一网络的精彩纷呈。需要事先声明的是,关于无标度网络研究的文献众多,从经验验证到建模、从特征分析到控制等。即使是关于其定义本身的研究也有包括我国学者史定华教授在内的一些学者的工作。本文远非无标度网络研究历史的完整记录,而只是围绕着本文的主题,选取其中我们认为有关联的少数节点加以阐述。
HTML
[1] | ALBERT R, JEONG H, BARABÁSI A-L. Diameter of the world-wide web[J]. Nature, 1999, 401(6749): 130-131. | |
[2] | 艾伯特-拉斯洛·巴拉巴西. 网络科学[M]. 沈华伟, 黄俊铭, 译. 郑州: 河南科学技术出版社, 2020. | BARABÁSI A-L. Network science[M]. Translated by SHEN Hua-wei and HUANG Jun-ming. Zhengzhou: Henan Science and Technology Press, 2020. |
[3] | BARABÁSI A-L, ALBERT R. Emergence of scaling in random networks[J]. Science, 1999, 286(5439): 509-512. | |
[4] | WATTS D J, STROGATZ S H. Collective dynamics of ‘small-world’ networks[J]. Nature, 1998, 393(6684): 440-442. | |
[5] | FORTUNATO S, BERGSTROM C T, BÖRNER K, et al. Science of science[J]. Science, 2018, 359(6379): eaao01851-eaao01857. | |
[6] | ZENG A, SHEN Z, ZHOU J, et al. The science of science: From the perspective of complex systems[J]. Physics Reports, 2017, 714: 1-73. | |
[7] | GATES A J, KE Q, VAROL O, et al. Nature’s reach: Narrow work has broad impact[J]. Nature, 2019, 575: 32-34. | |
[8] | 李约瑟, 王铃, D J 普拉斯, 等. 科学史与科学家介绍——中国的天文钟[J]. 科学通报, 1956(6): 103-104. | NEEDHAM J T M, WANG Ling, PRICE D J de S, et al. The introduction of history of science and the scientists: The chronometer of China[J]. Cinese Science Bulletin, 1956(6): 103-104. |
[9] | PRICE D J de S. Science since Babylon[M]. New Haven: Yale University Press, 1961. | |
[10] | PRICE D J de S. Little science, big science[M]. Boston, MA: Columbia University Press, 1963. | |
[11] | GARFIELD E. In tribute to Derek John de Solla Price: A citation analysis of little science, big sicence[J]. Scientometrics, 1985, 7(3-6): 487-503. | |
[12] | WANG Da-shun, BARABÁSI A-L. Science of science[M]. Cambridge: Cambridge University Press, 2020. | |
[13] | PRICE D J de S. Networks of scientific papers[J]. Science, 1965, 149: 510-515. | |
[14] | PRICE D J de S. A general theory of bibliometric and other cumulative advantage processes[J]. Journal of the American Society for Information Science, 1976, 27(5): 292-306. | |
[15] | NEWMAN M. Networks: An introduction[M]. Oxford: Oxford University Press, 2010. | |
[16] | WATTS D J. Six degrees: The science of a connected age[M]. London: W.W. Norton & Company, 2004. | |
[17] | SIMON H A. On a class of skew distribution functions[J]. Biometrika, 1955, 42(3/4): 425-440. | |
[18] | YULE G U. A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis, F.R.S.[J]. Trans R Soc B, 1924, 213: 21-87. | |
[19] | EGGENBERGER F, PÓLYA G. Über die satistik verketteter vorgänge[J]. Zamm‐Journal of Applied Mathematics & Mechanics, 1923, 3(4): 279-289. | |
[20] | MITZENMACHER M. A brief history of generative models for power law and lognormal distributions[J]. Internet Mathematics, 2004, 1(2): 226-251. | |
[21] | FALOUTSOS M, FALOUTSOS P, FALOUTSOS C. On power-law relationships of the internet topology[J]. ACM SIGCOMM Computer Communication Review, 1999, 29(4): 251-262. | |
[22] | CARLSON J M, DOYLE J. Highly optimized tolerance: A mechanism for power laws in designed systems[J]. Physical Review E, 1999, 60(2): 1412. | |
[23] | FABRIKANT A, KOUTSOUPIAS E, PAPADIMITRIOU C H. Heuristically optimized trade-offs: A new paradigm for power laws in the Internet[C]//International Colloquium on Automata, Languages, and Programming. Berlin: Springer, 2002: 110-122. | |
[24] | MANDELBROT B. An informational theory of the statistical structure of language[J]. Communication Theory, 1953, 84: 486-502. | |
[25] | ZIPF G K. Human behavior and the principle of least effort: An introduction to human ecology[M]. Boston: Addison-Wesley Press, 1949. | |
[26] | 迈克尔·巴蒂. 创造未来城市[M]. 徐蜀辰, 陈珝怡, 译. 北京: 中信出版集团, 2020. | BATTY M. Inventing future cities[M]. Translated by XU Shu-chen and CHEN Xu-yi. Beijing: CITIC Press Group, 2020. |
[27] | KRUGMAN P. Confronting the mystery of urban hierarchy[J]. Journal of the Japanese & International Economies, 1996, 10(4): 399-418. | |
[28] | PARETO V. The new theories of economics[J]. Journal of Political Economy, 1897, 5(4): 485-502. | |
[29] | MANDELBROT B. A note on a class of skew distribution functions: Analysis and critique of a paper by HA Simon[J]. Information and Control, 1959, 2(1): 90-99. | |
[30] | SIMON H A. Models of my life[M]. Cambridge, Massachusetts: The MIT Press, 1996. | |
[31] | MANDELBROT B. The fractalist: Memoir of a scientific maverick[M]. Manhattan: Pantheon Books, 2012. | |
[32] | SIMON H A. Some further notes on a class of skew distribution functions[J]. Information and Control, 1960, 3(1): 80-88. | |
[33] | MANDELBROT B. Final note on a class of skew distribution functions: Analysis and critique of a model due to HA Simon[J]. Information and Control, 1961, 4(2-3): 198-216. | |
[34] | SIMON H A. Reply to "final note" by Benoit Mandelbrot[J]. Information and Control, 1961, 4(2-3): 217-223. | |
[35] | MANDELBROT B. Post scriptum to "final note"[J]. Information and Control, 1961, 4(2-3): 300-304. | |
[36] | SIMON H A. Reply to Dr. Mandelbrot's post scriptum[J]. Inf Control, 1961, 4(2-3): 305-308. | |
[37] | KORNAI A. Mathematical linguistics[M]. Berlin: Springer Science & Business Media, 2007. | |
[38] | KRUGMAN P. The self-organizing economy[M]. Cambridge MA: Blackwell Publishers, 1996. | |
[39] | PAPADOPOULOS F, KITSAK M, SERRANO M Á, et al. Popularity versus similarity in growing networks[J]. Nature, 2012, 489(7417): 537-540. | |
[40] | BARABÁSI A-L. Luck or reason[J]. Nature, 2012, 489(7417): 507-508. | |
[41] | CLAUSET A, SHALIZI C R, NEWMAN M E J. Power-law distributions in empirical data[J]. SIAM Review, 2009, 51(4): 661-703. | |
[42] | BROIDO A D, CLAUSET A. Scale-free networks are rare[J]. Nature Communications, 2019, 10(1017): 1-10. (arXiv preprint arXiv: 1801.03400, 2018). | |
[43] | KLARREICH E. Scant evidence of power laws found in real-world networks[EB/OL]. (2018-02-15). https://www.quantamagazine.org/scant-evidence-of-power-laws-found-in-real-world-networks-20180215/. | |
[44] | BARABÁSI A-L. Love is all you need—Clauset's fruitless search for scale-free net works[EB/OL]. (2018-03-06). https://www.barabasilab.com/post/love-is-all-you-need? from=groupmessage&isappinstalled=0. | |
[45] | VOITALOV I, VAN D H P, VAN D H R, et al. Scale-free networks well done[J]. Physical Review Research, 2019, 1(3): 033034. (arXiv preprint arXiv: 1811.02071, 2018). | |
[46] | KRIOUKOV D. The proof of innocence[EB/OL]. (2012-04-01). https://arxiv.org/abs/1204.0162. | |
[47] | HOLME P. Rare and everywhere: Perspectives on scale-free networks[J]. Nature Communications, 2019, 10: 1016. | |
[48] | STUMPF M P H, PORTER M A. Critical truths about power laws[J]. Science, 2012, 335(6069): 665-666. | |
[49] | AMARAl L A N, GUIMERA R. Lies, damned lies and statistics[J]. Nature Physics, 2006, 2(2): 75-76. | |
[50] | LI T Y, YORKE J A. Period three implies chaos[J]. The American Mathematical Monthly, 1975, 82(10): 985-992. | |
[51] | SHARKOVSKII A N. Coexistence of cycles of a continuous map of the line into itself[J]. Urain Mat Zh, 1964, 16(1): 61-71. |