A Local Clustering Algorithm for Connection Graphs

We give a clustering algorithm for connection graphs, that is, weighted graphs in which each edge is associated with a d-dimensional rotation. The problem of interest is to identify subsets of small Cheeger ratio that have a high level of consistency, i.e., that have a small edge boundary and for which the rotations along any distinct paths joining two vertices are the same or within some small error factor. We use PageRank vectors as well as tools related to the Cheeger constant to give a clustering algorithm that runs in nearly linear time.