On Small World Graphs in Non-uniformly Distributed Key Spaces

In this paper we show that the topologies of most logarithmic-style P2P systems like Pastry, Tapestry or P-Grid resemble small-world graphs. Inspired by Kleinberg’s small-world model [7] we extend the model of building "routing-efficient" small-world graphs and propose two new models. We show that the graph, constructed according to our model for uniform key distribution and logarithmic outdegree, will have similar properties as the topologies of structured P2P systems with logarithmic outdegree. Moreover, we propose a novel model of building graphs which support uneven node distributions and preserves all desired properties of Kleinberg’s small-world model. With such a model we are setting a reference base for nowadays emerging P2P systems that need to support uneven key distributions.