Ağ Teorisinin Temelleri ve Evrimi: Bütünsel Bir Değerlendirme

Abstract

Geçtiğimiz yıllar içerisinde pek çok fizikçi, internet teorisyeni ve sosyal bilimci, ağ teorisinin geliştirilmesinde önemli adımlar atmışlardır. Bu teori ve onun giderek artan bir şekilde ağ bilimi olarak adlandırılan ampirik temeli, ağların neden ortaya çıktığını, nasıl büyüdüklerini ve geliştiklerini açıklamaya çalışmaktadır. Ağ perspektifi, biyoloji, sosyal bilimler, bilgi bilimleri, ekonomik ve diğer alanlar hakkında derin soruların ele alınmasını sağlar. Ağ bilimi sosyal ağlar, internet, karayolları ve terörist ağlarını da kapsayan çeşitli ağlarda muazzam benzerlikler olduğunu göstermiştir. Günümüzde büyük ölçekli ağları anlayabilmek için ağ bilimine disiplinler arası bir yaklaşım gerekmektedir. Örneğin matematik bilimcileri yol uzunlukları, derece dağılımları ve korelasyon katsayıları gibi ağın istatistiksel yapısına odaklanmışlardır. Bir araştırma alanında geliştirilen ölçüm, modelleme veya görselleştirme algoritmaları ağlar hakkındaki kavrayışı arttırmaktadır. Ağdaki bağlantılar insanların öğrenme, fikir oluşturma, haber toplama yöntemlerini ve hastalığın yayılması gibi pek çok olayı etkiler. Bu ağların yapısı hakkında yeterince bilgi elde edilmediği taktirde, ilgili sistemlerin tam olarak nasıl çalıştığını anlamak mümkün değildir. Bu bağlamda ağlar önemlidir çünkü ağlar anlaşılmaz ise piyasaların nasıl işlediği, kuruluşların sorunlarını nasıl çözdüğü veya toplumların nasıl değiştiğini anlamak mümkün değildir. Bu nedenle çalışmada öncelikli olarak ağ teorisinin teorik ve kavramsal çerçevesi incelenmiştir. Ardından geçmişten günümüze ağ teorisi ile ilgili önemli olayların tarihsel zaman çizelgesine bakılıp, ağ teorisinin istatistiksel temeli, ilkeleri, felsefesi ve matematiği ele alınmıştır.

Keywords

• Ağ teorisi
• Ağ Tarihçesi
• Temel Kavramlar
• Teorik Modeller

Fundamentals and Evolution of Network Theory: A Holistic Evaluation

Abstract

Over the past years, many physicists, internet theorists, and social scientists have made significant strides in the development of network theory. This theory and its empirical basis, increasingly referred to as network science, attempts to explain why networks arise and how they grow and evolve. The network perspective enables deep questions to be addressed in biology, social sciences, economics and other fields. Network science has shown tremendous similarities in various networks, including social networks, the internet and terrorist networks. An interdisciplinary approach to network science is required to understand large-scale networks today. For example, mathematicians have focused on the statistical structure of the network, such as path lengths, degree distributions, and correlation coefficients. Measurement, modeling or visualization algorithms developed in a research area increase the understanding of networks. Connections in the network influence the way people learn, form opinions, gather news, and many things, such as the spread of disease. Unless enough information is obtained about the structure of these networks, it is not possible to understand exactly how the related systems work. In this context, networks are important because if networks are not understood, it is not possible to understand how markets work, how organizations solve their problems or how societies change. For this reason, the theoretical and conceptual framework of network theory is primarily examined in this study. Then, the historical timeline of important events related to network theory from past to present is examined, and the statistical basis, principles, philosophy and mathematics of network theory are discussed.

Keywords

• Network Science
• Network History
• Basic Concepts
• Theoretical Models

References

1. Albert, R. and Barabási, A. L., 2002. Statistical mechanics of complex networks. Reviews of Modern Physics, 74(1), 47.
2. Albert, R., Jeong, H. and Barabási, A. L., 1999. Diameter of the world-wide web. Nature, 401(6749), 130-131.
3. Albert, R., Jeong, H. and Barabási, A. L., 2000. Error and attack tolerance of complex networks. Nature, 406(6794), 378.
4. Anderson, R. M., 1991. Discussion: the Kermack-McKendrick epidemic threshold theorem. Bulletin of Mathematical Biology, 53(1), 1-32.
5. Appa Rao, G. and Singh, S. N., 1980. Structural and functional analysis of interpersonal communication networks in diffusion of high yielding rice varieties in two villages [India]. Oryza (India).
6. Atay, F. M., Biyikoglu, T. and Jost, J., 2006. Synchronization of networks with prescribed degree distributions. IEEE Transactions on Circuits and Systems I: Regular Papers, 53(1), 92-98.
7. Baker, W. E., 1984. The social structure of a national securities market. American Journal of Sociology, 89(4), 775-811.
8. Barabási, A.L. and Albert, R., 1999. Emergence of Scaling in Random Networks. Science, 286(5439), 509-512.

9. Barabási, A.L., 2003. Linked: How everything is connected to everything else and what it means for business, science and everyday life. Penguin Group, New York.
10. Barabási, A. L. and Elhüseyni, N. (2010). İş hayatında, bilimde ve günlük yaşamda bağlantılar. Optimist Yayım Dağıtım.
11. Barabási, A. L., 2016. Network science. Cambridge University Press.
12. Bass, F. M., 1969. A new product growth for model consumer durables. Management science, 15(5), 215-227.
13. Bollobás, B., Riordan, O., Spencer, J. and Tusnády, G., 2011. The degree sequence of a scale-free random graph process. In The Structure and Dynamics of Networks, 384-395.
14. Borgatti, S. P., Everett, M. G. and Johnson, J. C., 2018. Analyzing social networks. Sage.
15. Börner, K., Sanyal, S., and Vespignani, A. (2007). Network science. Annual review of information science and technology, 41(1), 537-607.
16. Brauer, F., 2005. The Kermack–McKendrick epidemic model revisited. Mathematical Biosciences, 198(2), 119-131.
17. Burt, R. S., 1982. Toward a structural theory of action: Network models of social structure, perception, and action. New York: Academic Press.
18. Burt, R., 2005. Broker age and closure: An introduction to social capital. Oxford: Oxford University Press.
19. Calvert, K. L., Doar, M. B. and Zegura, E. W., 1997. Modeling internet topology. IEEE Communications Magazine, 35(6), 160-163.
20. Chang, H., Su, B. B., Zhou, Y. P. and He, D. R., 2007. Assortativity and act degree distribution of some collaboration networks. Physica A: Statistical Mechanics and its Applications, 383(2), 687-702.
21. Clauset, A., Moore, C. and Newman, M. E., 2006. Structural inference of hierarchies in networks. In ICML Workshop on Statistical Network Analysis. Springer, Berlin, Heidelberg.
22. Cross, R., Parker, A. and Sasson, L. (Eds.)., 2003. Networks in the knowledge economy. Oxford University Press.
23. De Blasio, B. F.,Svensson, Å. and Liljeros, F., 2007. Preferential attachment in sexual networks. Proceedings of the National Academy of Sciences, 104(26), 10762-10767.
24. De Nooy, W., Mrvar, A. and Batagelj, V., 2018. Exploratory social network analysis with Pajek: Revised and expanded edition for updated software (Vol. 46). Cambridge University Press.
25. De Tarde, G., 1903. The laws of imitation. H. Holt.
26. Erdős, P. and Rényi, A., 1959. Some further statistical properties of the digits in Cantor's series. Acta Mathematica Academiae Scientiarum Hungarica, 10(1-2), 21-29.
27. Erdős, P. and Rényi, A., 1961. On the strength of connectedness of a random graph. Acta Mathematica Hungarica, 12(1), 261-267.
28. Estrada, E., Fox, M., Higham, D. J. and Oppo, G. L. (Eds.)., 2010. Network science: complexity in nature and technology. Springer Science and Business Media.
29. Faloutsos, M., Faloutsos, P. and Faloutsos, C., 1999. On power-law relationships of the internet topology. ACM SIGCOMM Computer Communication Review, 29(4), 251-262.
30. Fienberg, S. E., 2012. A brief history of statistical models for network analysis and open challenges. Journal of Computational and Graphical Statistics, 21(4), 825-839.
31. Fisher, J.C. and Pry, R.H., 1971. A simple substitution model of technological change. Technological Forecasting and Social Change, 88(3), 75-88.
32. Freeman, L. C., 1978. Centrality in social networks conceptual clarification. Social networks, 1(3), 215-239.
33. Friedkin, N. E., 1980. A test of structural features of Granovetter’s strength of weak ties theory. Social Networks, 2(22), 41.
34. Friesz, T. L. (Ed.)., 2007. Network science, nonlinear science and infrastructure systems (Vol. 102). Springer Science and Business Media.
35. Gabbay, M., 2007. The effects of nonlinear interactions and network structure in small group opinion dynamics. Physica A: Statistical Mechanics and its Applications, 378(1), 118-126.
36. Gilbert, E. N., 1959. Random graphs. The Annals of Mathematical Statistics, 30(4), 1141-1144.
37. Granovetter, M. S., 1973. The strength of weakties. American Journal of Sociology, 78, 1360–1380.
38. Granovetter, M., 1982. “The Strength of Weak Ties: A Network Theory Revisited”. In P. V. Marsden and Nan Lin, eds. Social Structure and Network Analysis. Beverly Hills: Sage.
39. Granovetter, M., 1985. Economic action and social structure: The problem of embeddedness. American Journal of Sociology, 91(3), 481-510.
40. Gürsakal, N., Tüzüntürk, S. and Sert, F., 2014. Sosyal ağ verilerinin kuvvet yasası olasılık dağılımına uygunluk analizi: twitter örneği. 15. Uluslararası Ekonometri, Yöneylem ve İstatistik Sempozyumu Bildiriler Kitabı, 464-482.
41. Hanneman, R. A. and Riddle, M., 2005. Introduction to social network methods.
42. Hashimoto, Y., 2016. Growth fluctuation in preferential attachment dynamics. Physical Review E, 93(4), 042130.
43. Haythornthwaite, C., 2005. Social network methods and measures for examining e-learning. Social networks, 1-22.
44. Hennig, M., Brandes, U., Pfeffer, J. and Mergel, I., 2012. Studying social networks: A guide to empirical research. Campus Verlag.
45. Hoelscher, C., 2019. Degrees of separation in annie baker’s the flick.
46. Huang, C. Y., Sun, C. T., Hsieh, J. L. and Lin, H., 2004. Simulating SARS: Small-World epidemiological modeling and public health policy assessments. Journal of Artificial Societies and Social Simulation, 7(4).
47. Huang, C. Y., Sun, C. T. and Lin, H. C., 2005. Influence of local information on social simulations in small-world network models. Journal of Artificial Societies and Social Simulation, 8(4).
48. Karsai, M., Kivelä, M., Pan, R. K., Kaski, K., Kertész, J., Barabási, A. L. and Saramäki, J., 2011. Small but slow world: How network topology and burstiness slow down spreading. Physical Review E, 83(2), 025102.
49. Kim, H., Toroczkai, Z., Erdős, P. L., Miklós, I. and Székely, L. A., 2009. Degree-based graph construction. Journal of Physics A: Mathematical and Theoretical, 42(39), 392001.
50. Kleinberg, J., 2000. The small-world phenomenon: An algorithmic perspective. In Proceedings of The Thirty-Second Annual ACM Symposium on Theory of Computing, 163-170.
51. Kleinfeld, J. S., 2002. The small world problem. Society, 39(2), 61.
52. Kolaczyk, E. D., 2013. Statistical analysis of network data, SAMSI program on Complex networks. Boston University.
53. Kretzschmar, M. and Morris, M., 1996. Measures of concurrency in networks and the spread of infectious disease. Mathematical Biosciences, 133(2), 165-195.
54. Leskovec, J. and Horvitz, E., 2008. Planetary-scale views on a large instant-messaging network. In Proceedings of The 17th International Conference on World Wide Web, 915-924.
55. Lewis, T. G., 2011. Network science: Theory and applications. John Wiley and Sons.
56. Lézoray, O. and Grady, L., 2012. Image processing and analysis with graphs: theory and practice. CRC Press.
57. Liu, W. T. and Duff, R. W., 1972. The strength in weak ties. Public Opinion Quarterly, 36(3), 361-366.
58. Milgram, S., 1967. The small world problem. Psychology Today, 2(1), 60-67.
59. Montgomery, J. D., 1992. Job search and network composition: Implications of the strength-of-weak-ties hypothesis. American Sociological Review, 586-596.
60. Moreno, J. L., 1934. Who shall survive?: A new approach to the problem of human interrelations.
61. National Research Council., 2005. Network Science Committee on Network Science for Future Army Applications.
62. Nelson, R. E., 1986. Social networks and organizational interventions: Insights from an area-wide labor-management committee. The Journal of Applied Behavioral Science, 22(1), 65-76.
63. Nelson, R. E., 1989. The strength of strong ties: Social networks and intergroup conflict in organizations. Academy of Management Journal, 32(2), 377-401.
64. Newman, M. E. and Watts, D. J., 1999a. Renormalization group analysis of the small-world network model. Physics Letters A, 263, 341-346.
65. Newman, M. E., Watts, D. J. and Strogatz, S. H., 2002. Random graph models of social networks. Proceedings of The National Academy of Sciences, 99(1), 2566-2572.
66. Newman, D., 2003. On borders and power: A theoretical framework. Journal of Borderlands Studies, 18(1), 13-25.
67. Newman, M.E.J., 2010. Networks: An introduction. New York: Oxford University Press.
68. Otte, E. and Rousseau, R., 2002. Social network analysis: a powerful strategy, also for the information sciences. Journal of Information Science, 28(6), 441-453.
69. Pastor-Satorras, R. and Vespignani, A., 2001. Epidemic spreading in scale-free networks. Physical Review Letters, 86(14), 3200.
70. Poole, M. S. and Hollingshead, A. B. (Eds.), 2014. Theories of small groups: Interdisciplinary perspectives. Sage Publications.
71. Prell, C., 2012. Social network analysis: History theory and methodology. Los Angeles etc.
72. 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.
73. Pržulj, N., 2007. Biological network comparison using graphlet degree distribution. Bioinformatics, 23(2), 177-183.
74. Rapoport, A., 1951. Nets with distance bias. The Bulletin of Mathematical Biophysics, 13(2), 85-91.
75. Rogers, E. M., 2003. Diffusion networks. Networks in The Knowledge Economy, 130-179.
76. Rost, K., 2011. The strength of strong ties in the creation of innovation. Research Policy, 40(4), 588-604.
77. Sabah, L., Dalı, B. M. A. and Şimşek, D., 2018. Sosyal Ağ Analizi Ve Salgın Modelleme.
78. Schneider, H. L. and Huber, L. M., 2008. Social networks: Development, evaluation and ınfluence. Nova Science Publishers.
79. Scott, A. J., 2000. The cultural economy of cities: Essays on the geography of image-producing industries. Sage.
80. Seker, S. E., 2015. Çizge teorisi. YBS Ansiklopedi, 17-29.
81. Sekharaiah, K. C. and Khan, M. M., 2009. Towards metrics for social computing. Proceedings of World Academy of Science, Engineering, and Tec, 37(2070-3740), 1086-1090.
82. Tonelli, R., Concas, G., & Locci, M. (2010). Three efficient algorithms for implementing the preferential attachment mechanism in Yule-Simon Stochastic Process. WSEAS Trans. Inf. Sci. App, 7(2), 176-185.
83. Tunalı, V., 2016. Sosyal Ağ Analizine Giriş. Ankara: Nobel Yayıncılık.
84. Tüzüntürk, S., 2012. Ağ bilimi. Dora Yayınları.
85. Wang, X. F. and Chen, G., 2003. Complex Networks: Small-World, Scale-Free and Beyond. IEEE Circuits and Systems Magazine, First Quarter, 6-20.
86. Wasserman, S. and Faust, K., 1994. Social network analysis: Methods and applications (Vol. 8). Cambridge university press.
87. Watts, D. J. and Strogatz, S. H., 1998. Collective dynamics of 'Small-World' networks. Nature, 393(6684), 440-442.
88. Watts, R. A., Lane, S. E., Bentham, G. and Scott, D. G., 2000. Epidemiology of systemic vasculitis: a ten‐year study in the United Kingdom. Arthritis and Rheumatism: Official Journal of the American College of Rheumatology, 43(2), 414-419.
89. Weinmann, G., 1980. Conversation networks as communication networks. University of Haifa, Israel.
90. Wellman, B., and Berkowitz, S. D. (Eds.)., 1988. Social structures: A network approach (Vol. 2). CUP Archive.
91. Xia, Y., Fan, J. and Hill, D., 2010. Cascading failure in Watts–Strogatz small-world networks. Physica A: Statistical Mechanics and its Applications, 389(6), 1281-1285.
92. Zhang, B. and Horvath, S., 2005. A general framework for weighted gene co-expression network analysis. Statistical Applications in Genetics and Molecular Biology, 4(1).
93. Zhang, L. and Tu, W., 2009. Six degrees of separation in online society.