the circular area. As this circle gets expanded further out, the number of nodes in the given area increases proportional to as the probability of having a random link with any node remains proportional , meaning the probability of the original node having a weak tie with any node a given distance away is effectively independent of distance. Therefore, it is concluded that with , long-range edges are evenly distributed over all distances, which is effective for letting us funnel to our final destination. Some structured Peer-to-peer systems based on DHTs often are implementing variants of Kleinberg's Small-World topology to enable efficient routing within Peer-to-peer network with limited node degrees. See also References Network theory