Estimation of Length of Node-to-Node Paths Distribution in the Global Network

Abstract

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. ‘e 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 Barabasi–Albert ´ model. Several most viable hypotheses explaining diffierences in skewness and kurtosis of experimentally obtained pathlength distribution estimations and values derived from the Barabasi–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
• node-to-node distance distribution
• experiment
• baraba´si–albert model