Butterfly counting and bitruss decomposition on uncertain bipartite graphs

Uncertain butterflies are one of, if not the, most important graphlet structures on uncertain bipartite networks. In this paper, we examine the uncertain butterfly structure (in which the existential probability of the graphlet is greater than or equal to a threshold parameter), as well as the global Uncertain Butterfly Counting Problem (to count the total number of these instances over an entire network). To solve this task, we propose a non-trivial exact baseline (UBFC), as well as an improved algorithm (IUBFC) which we show to be faster both theoretically and practically. We also design two sampling frameworks (UBS and PES) which can sample either a vertex, edge or wedge from the network uniformly and estimate the global count quickly. Furthermore, a notable butterfly-based community structure which has been examined in the past is the k-bitruss. We adapt this community structure onto the uncertain bipartite graph setting and introduce the Uncertain Bitruss Decomposition Problem (which can be used to directly answer any k-bitruss search query for any k). We then propose an exact algorithm (UBitD) to solve our problem with three variations in deriving the initial uncertain support. Using a range of networks with different edge existential probability distributions, we validate the efficiency and effectiveness of our solutions. © 2023, The Author(s).