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Butterflies are an important motif found in bipartite graphs that provide a structural way for finding dense regions within the graph. Beyond counting butterflies and enumerating them, other metrics and peeling for bipartite graphs are designed around counting butterfly motifs. The importance of counting butterflies has led to many works on efficient implementations for butterfly counting, given certain situational or hardware constraints. However, most algorithms are based on first counting the building block of the butterfly motif, and from that calculating the total possible number of butterflies in the graph. In this paper, using a linear algebra approach, we show that many provably correct algorithms for counting butterflies can be systematically derived. Moreover, we show how this formulation facilitates butterfly peeling algorithms that find the k-tip and k-wing subgraphs within a bipartite graph.
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Butterfly Counting in Bipartite Networks
We consider the problem of counting motifs in bipartite affiliation networks, such as author-paper, user-product, and actor-movie relations. We focus on counting the number of occurrences of a "butterfly", a complete 2x2 biclique, the simplest cohesive higher-order structure in a bipartite graph. Our main contribution is a suite of randomized algorithms that can quickly approximate the number of butterflies in a graph with a provable guarantee on accuracy. An experimental evaluation on large real-world networks shows that our algorithms return accurate estimates within a few seconds, even for networks with trillions of butterflies and hundreds of millions of edges.
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- Award ID(s):
- 1725702
- PAR ID:
- 10073154
- Date Published:
- Journal Name:
- Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining
- Page Range / eLocation ID:
- 2150 to 2159
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3219819.3220097
