This paper investigates graph clustering in the planted cluster model in the presence of small clusters. Traditional results dictate that for an algorithm to provably correctly recover the clusters, all clusters must be sufciently large (in particular, ( p n) where n is the number of nodes of the graph). We show that this is not really a restriction: by a more rened analysis of the trace-norm based matrix recovery approach proposed in Jalali et al. (2011) and Chen et al. (2012), we prove that small clusters, under certain mild assumptions, do not hinder recovery of large ones. Based on this result, we further devise an iterative algorithm to recover almost all clusters via a \peeling strategy", i.e., recover large clusters
['Nir Ailon', 'Yudong Chen', 'Huan Xu']
Breaking the Small Cluster Barrier of Graph Clustering