In this paper we present a method called local hub screening for detecting hubs in a sparse correlation or partial correlation network over <i>p</i> nodes. The proposed method is related to hub screening<sup>1</sup> where a Poisson-type limit is used to specify <i>p</i>-values on the number of spurious hub nodes found in the network. In this paper we also establish Poisson limits. However, instead of being on the global number of hub nodes found, here the Poisson limit applies to the node degree found at an individual node. This allows us to de ne asymptotic p-values that are local to each node. We will see that the convergence rates for proposed local hub screening method are at least a factor of <i>p</i> faster than those of global correlation and hub screening.