Geodesic
Estimation of length of node-to-node paths distribution in the global network
Modelirovanie i analiz informacionnyh sistem, Tome 27 (2020) no. 1, pp. 6-21 Cet article a éte moissonné depuis la source Math-Net.Ru

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The experiment aimed at finding a distribution of path lengths between nodes in the global network and an estimation of parameters of that distribution is described. In particular, the method of measurement of path length with traceroute utility of the GNU/Linux system and limitations on the selection of nodes imposed by traceroute are described. The measurement results are provided and high values of skewness and kurtosis for all resulting distributions are noted. Simulation model of this experiment was developed to test the experiment validity in the determination of distribution parameters in the global network. This model is also described. It is shown that high values of skewness and kurtosis of the measured distributions are not the result of the measurement technique, therefore the global network could not be described by the Barabási-Albert model. Several most viable hypotheses explaining diffierences in skewness and kurtosis of experimentally obtained pathlength distribution estimations and values derived from the Barabási-Albert model are listed. Results of diffierent hypotheses simulations are provided. It is shown that the most fitting hypothesis is that definitive influence on skewness and kurtosis of path-length distribution estimations is caused by the quasi pre-fractal structure of the global network.
Keywords: global network, routing, experiment
Mots-clés : node-to-node distance distribution, Barabási-Albert model. 
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A. I. Kononova; A. V. Gorodilov. Estimation of length of node-to-node paths distribution in the global network. Modelirovanie i analiz informacionnyh sistem, Tome 27 (2020) no. 1, pp. 6-21. http://geodesic.mathdoc.fr/item/MAIS_2020_27_1_a0/

[1] A. Gorodilov, A. Kononova, V. Shangin, “Osobennosti peredachi dannyh v decentralizovannyh piringovyh setyah”, Proceedings of Universities. Electronics, 98:6 (2012), 95–97

[2] A. P. Shiryaev, A. V. Dorofeev, A. R. Fedorov, L. G. Gagarina, V. V. Zaycev, “LDA models for finding trends in technical knowledge domain”, 2017 IEEE conference of Russian Young researchers in electrical and electronic engineering (EIConRus), 2017, 551–554

[3] D. Easley, J. Kleinberg, Networks, crowds, and markets: reasoning about a highly connected world, Cambridge University Press, 2010 | MR | Zbl

[4] A. Fronczak, P. Fronczak, J. A. Hołyst, “Average path length in random networks”, Physical Review E, 70:5 (2004), 056110

[5] R. Sedgewick, Algorithms in C, v. 5, Graph algorithms, Addison-Wesley Publishing Co, New York, USA, 2002 | MR

[6] H. Jeong, B. Tombor, Z. N. Albert, R.and Oltvai, A. Barabási, “The large-scale organization of metabolic networks”, Nature, 407:6804 (2000), 651–654

[7] R. Albert, A. Barabási, “Statistical mechanics of complex networks”, Reviews of modern physics, 74:1 (2002), 47–97 | MR | Zbl

[8] A. Gorodilov, A.V. Kononova, “Simulation as tool of error assessment of experimental measurement of path-lengths distribution in global network”, Sistemy komp'yuternoj matematiki i ih prilozheniya, materialy XX Mezhdunarodnoj nauchnoj konferencii, v. 1, 2019, 34–41

[9] R. A. Kochkarov, D. A. Pavlov, D. A. Hubieva, “Fractal and preefactal graphs, basic definitions and symbols”, Scientific journal of KubSAU (Polythematic online scientific journal of Kuban State Agrarian University), 2017, no. 134, 174–188