Abstract
A fundamental problem in large-scale network analysis is finding and enumerating basic graph motifs. Graph motifs that represent the building blocks of certain networks can reveal the underlying structures of these networks. There has been recent work on designing efficient sequential algorithms for butterfly counting and peeling. Updating the bucketing structure involves moving elements to new buckets based on their updated butterfly counts, which can only decrease. There are two main methods to translate wedge counts into butterfly counts, per-vertex or per-edge. Side ordering outperforms the other rankings for itwiki and livejournal, while approximate complement degeneracy, approximate degree, and degree orderings outperform side ordering for discogs, enwiki, delicious, orkut, and web. There have been several sequential algorithms designed for butterfly counting and peeling. The ParButterfly framework is built with modular components that can be combined for practical efficiency.
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