Abstract
Small-world networks have received much attention recently. Computer scientists, theoretical physicists, mathematicians, and others use them as basis for their studies. At least partly due to the different mind-sets of these disciplines, these random graph models have not always been correctly applied to questions in, e.g., peer-to-peer computing. This paper tries to shed some light on common misunderstandings in the study of small-world peer-to-peer networks. It shows that, contrary to some recent publications, Gnutella can indeed be described by a model with power-law degree distribution. To further distinguish the proposed model from other random graph models, this paper also applies two mathematical concepts, dimension and curvature, to the study of random graphs. These concepts help to understand the distribution of node distances in small-world networks. It thus becomes clear that the observed deficit in the number of reachable nodes in Gnutella-like networks is quite natural and no sign of any wrong or undesirable effect like, e.g., network partitioning.
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References
Albert, R., Barabasi, A.-L.: Topology of evolving networks: Local events and universality. Physical Review Letters 85(24) (2000)
Albert, R., Barabasi, A.-L.: Statistical mechanics of complex networks. Review of Modern Physics 74(47) (2002)
Albert, R., Jeong, H., Barabasi, A.-L.: Diameter of the world wide web. Nature 401, 130–131 (1999)
Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)
Chen, Q., Chang, H., Govindan, R., Jamin, S., Shenker, S.J., Willinger, W.: The origin of power laws in internet topologies revisited. In: Proceedings of the 21st Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2002), vol. 2, pp. 608–617 (2002)
Erdös, P., Renyi, A.: On random graphs. Publ. Math. Debrecen 6, 290–297 (1959)
Erdös, P., Renyi, A.: On the evolution of random graphs. Publ. Math. Inst. Hungar. Acad. Sci. 5, 17–61 (1960)
Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationships of the internet topology. In: SIGCOMM, pp. 251–262 (1999)
Mandelbrot, B.B.: The Fractal Geometry of Nature. H. W. Freeman and Company, New York (1977)
Milgram, S.: The small world problem. Psychol. Today 2, 60–67 (1967)
Ripeanu, M., Foster, I.: Mapping gnutella network: Macroscopic properties of large-scale peer-to-peer systems. In: Proceedings of the First International Workshop on Peer-to-Peer Systems (IPTPS 2002), Cambridge, Massachusetts (March 2002)
Ripeanu, M., Foster, I., Iamnitchi, A.: Mapping the gnutella network: Properties of large-scale peer-to-peer systems and implications for system design. IEEE Internet Computing Journal (Special issue on peer-to-peer networking) 6(1) (2002)
Schollmeier, R., Hermann, F.: Topology-analysis of pure peer-to-peer networks. In: Proceedings of Kommunikation in Verteilten Systemen, Leipzig, Germany, February 26-28, pp. 359–370 (2003)
Schollmeier, R., Schollmeier, G.: Why peer-to-peer does scale: An analysis of P2P traffic patterns. In: Proceedings of the Second International Conference on Peer-to-Peer Computing, Linköping, Sweden, September 5-7, pp. 112–119 (2002)
Tutschku, K., deMeer, H.: A measurement study on the dynamics of gnutella overlays. In: Proceedings of Kommunikation in Verteilten Systemen, Leipzig, Germany, February 26-28, pp. 295–306 (2003)
Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393, 440–442 (1998)
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Fuhrmann, T. (2003). Small-World Networks Revisited. In: Böhme, T., Heyer, G., Unger, H. (eds) Innovative Internet Community Systems. IICS 2003. Lecture Notes in Computer Science, vol 2877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39884-4_7
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DOI: https://doi.org/10.1007/978-3-540-39884-4_7
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