Peer-to-peer networks based on random transformations of connected regular undirected graphs
Peter Mahlmann, Christian Schindelhauer · 2005
We present k-Flipper, a graph transformation algorithm that transforms regular undirected graphs. Given a path of k+2 edges it interchanges the end vertices of the path. By definition this operation preserves regularity and connectivity. We show that every regular connected graph can be reached by a series of these operations for all k ¡Ý 1. We use a randomized version, called Random k-Flipper, in order to create random regular connected undirected graphs that may serve as a backbone for peer-to-peer networks. We prove for degree d¡Ê ¦¸(log n) that a series of O(dn) Random k-Flipper operations with k ∈ ¦¨(d2n2 log 1/¦Å) transforms any graph into an expander graph with high probability, i.e. 1-n-¦¨(1).