Temporal bipartite graphs are widely used to denote time-evolving
relationships between two disjoint sets of nodes, such as customer-product
interactions in E-commerce and user-group memberships in social networks.
Temporal butterflies, (2,2)-bicliques that occur within a short period and in
a prescribed order, are essential in modeling the structural and sequential
patterns of such graphs. Counting the number of temporal butterflies is thus a
fundamental task in analyzing temporal bipartite graphs. However, existing
algorithms for butterfly counting on static bipartite graphs and motif counting
on temporal unipartite graphs are inefficient for this purpose. In this paper,
we present a general framework with three sampling strategies for temporal
butterfly counting. Since exact counting can be time-consuming on large graphs,
our approach alternatively computes approximate estimates accurately and
efficiently. We also provide analytical bounds on the number of samples each
strategy requires to obtain estimates with small relative errors and high
probability. We finally evaluate our framework on six real-world datasets and
demonstrate its superior accuracy and efficiency compared to several baselines.
Overall, our proposed framework and sampling strategies provide efficient and
accurate approaches to approximating temporal butterfly counts on large-scale
temporal bipartite graphs.Comment: 10 pages, 10 figures; under revie