Before revision:  Finally, and most importantly, our method is strongly-local, meaning that its runtime depends only on the size of an input set. In practice this allows our method to quickly find localized clusters without exploring an entire input hypergraph . We demonstrate the power of our method in local cluster detection experiments on an Amazon product hypergraph and a Stack Overflow question hypergraph. Although both datasets involve millions of nodes, millions of edges, and a large average hyperedge size , we are able to detect local clusters in a matter of a few seconds or a few minutes , depending on the size of the cluster .
After revision:  Finally, and most importantly, our method is strongly-local, meaning that its runtime depends only on the size of the input set, and does not need to explore the entire hypergraph to find good local clusters. We use our methodology to effectively identify clusters in hypergraphs of real-world data with millions of nodes, millions of edges, and a large average hyperedge size , we are able to detect local clusters in a matter of a few seconds or a few minutes , depending on the size of the cluster .