( α , β )-bicliques serve to identify cohesive node groups in bipartite graphs, where each node is required to maintain at least α or β connections within the biclique. Although ( α , β )-biclique enumeration has been extensively studied, its temporal periodicity remains largely unexplored. To capture recurrent group behaviors in temporal bipartite graphs, we introduce the novel problem of periodic ( α , β )-biclique enumeration. Our approach presents three core innovations: First, a θ -periodic biclique model, which enforces that all edges within a biclique exhibit θ -periodic temporal support. Second, an edge-based reduction framework that avoids the combinatorial explosion typical in node-based enumeration. This is achieved by first constructing condensed subgraphs via θ -temporal edge filtering, followed by biclique enumeration within the reduced space. Third, two optimized data structures: (i) a linked edge list (LE-list)–based periodic edge aggregator that enables constant-time subgraph access, and (ii) a Trie-based periodicity detector that accelerates the validation of temporal recurrence. Extensive experiments on six real-world temporal networks demonstrate up to a 10 × speedup over baseline methods, highlighting substantial gains in efficiency, accuracy, and scalability.
Yang et al. (Fri,) studied this question.