Accelerated butterfly counting with vertex priority on bipartite graphs

Abstract Bipartite graphs are of great importance in many real-world applications. Butterfly, which is a complete $$2 \times 2$$ 2 × biclique, plays key role bipartite graphs. In this paper, we investigate the problem efficient counting number butterflies. The most advanced techniques based on enumerating wedges dominant cost Nevertheless, existing algorithms cannot efficiently handle large-scale This becomes bottleneck instead layer-priority-based techniques, propose vertex-priority-based paradigm $${\mathsf {BFC}}$$ BFC - {VP}}$$ VP to enumerate much fewer wedges; leads significant improvement time complexity state-of-the-art algorithms. addition, present cache-aware strategies further improve efficiency while theoretically retaining . We also show that our proposed can work external and parallel contexts. Moreover, study butterfly batch-dynamic Specifically, given graph G batch-update edges B , aim maintain butterflies To tackle problem, fast with optimizations for reducing computation Our extensive empirical studies demonstrate significantly outperform baseline solutions real datasets.