Clustering for metric graphs using the p-Laplacian

Abstract

We deal with the clustering problem in a metric graph. We look for two clusters, and to this end, we study the first nonzero eigenvalue of the p Laplacian on a quantum graph with Newmann or Kirchoff boundary conditions on the nodes. Then, an associated eigenfunction up provides two sets inside the graph, {up > 0} and {up < 0}, which define the clusters. Moreover, we describe in detail the limit cases p→∞and p→1+.