A Unifying Framework to Identify Dense Subgraphs on Streams: Graph Nuclei to Hypergraph Cores

Finding dense regions of graphs is fundamental in graph mining. We focus on the computation of dense hierarchies and regions with graph nuclei---a generalization of k-cores and trusses. Static computation of nuclei, namely through variants of 'peeling', are easy to understand and implement. However, many practically important graphs undergo continuous change. Dynamic algorithms, maintaining nucleus computations on dynamic graph streams, are nuanced and require significant effort to port between nuclei, e.g., from k-cores to trusses. We propose a unifying framework to maintain nuclei in dynamic graph streams. First, we show no dynamic algorithm can asymptotically beat re-computation, highlighting the need to experimentally understand variability. Next, we prove equivalence between k-cores on a special hypergraph and nuclei. Our algorithm splits the problem into maintaining the special hypergraph and maintaining k-cores on it. We implement our algorithm and experimentally demonstrate improvements up to 108 x over re-computation. We show algorithmic improvements on k-cores apply to trusses and outperform truss-specific implementations.