Abstract:Measuring and characterizing the topological properties of peer-to-peer networks will benefit the optimization, management of the P2P systems. It seems infeasible to capture a complete and precise snapshot of P2P overlay networks due to the variety of P2P protocols and dynamics of the servents. Studying the details of P2P protocols and analyzing the specific P2P overlay network instance become an alternative method for this goal. In this paper, the measured Gnutella network topology is basically taken as an example. The architecture and performance of the distributed crawling system (called D-Crawler system) with feedback mechanism is presented. The properties of degree-rank distributions and degree-frequency distributions of the measured topology graphs are analyzed in detail. The small world characteristics for Gnutella network are discussed. The results show that the P2P overlay network topology characters are closely related to the P2P protocols and clients' behaviors. Gnutella network shows different characters in each tier. The top level graphs fit the power law in degree-rank distribution, but follow the Gaussian function in degree-frequency distribution. The bottom level graphs show weak power law in its degree-rank distribution, but are power law in its degree-frequency distribution. Fitting results indicate that power law could fit better for the degree-rank distribution and degree-frequency distribution of bottom level graphs, Gaussian could describe the degree-frequency distribution of the top level graphs. Gnutella overlay network has the small world property, but it is not the scale-free network, its topology may have developed over time following a different set of growth processes from those of the BA (Barabási-Albert) model.