Distributed Routing in Small-World Networks

So called small-world networks -- clustered networks with small diameters -- are thought to be prevalent in nature, especially appearing in people's social interactions. Many models exist for this phenomenon, with some of the most recent explaining how it is possible to find short routes between nodes in such networks. Searching for such routes, however, always depends on nodes knowing what their and their neighbors positions are relative to the destination. In real applications where one may wish to search a small-world network, such as peer-to-peer computer networks, this cannot always be assumed to be true. We propose and explore a method of routing that does not depend on such knowledge, and which can be implemented in a completely distributed way without any global elements. The Markov Chain Monte-Carlo based algorithm takes only a graph as input, and requires no further information about the nodes themselves. The proposed method is tested against simulated and real world data.